Abstract: We have considered a cosmological model of the FRW universe with variable $G$ and $\Lambda$. The solutions have been obtained for flat model with particular form of cosmological constant. The cosmological parameters have also been obtained for dust, radiation and stiff matter. The statefinder parameters are analyzed and have shown that these depends only on $w$ and $\epsilon$. Further the lookback time, proper distance, luminosity distance and angular diameter distance have also been calculated for our model.

Abstract: We derive the relationship of the redshift and the angular diameter distance to the average expansion rate for universes which are statistically homogeneous and isotropic and where the distribution evolves slowly, but which have otherwise arbitrary geometry and matter content. The relevant average expansion rate is selected by the observable redshift and the assumed symmetry properties of the spacetime. We show why light deflection and shear remain small. We write down the evolution equations for the average expansion rate and discuss the validity of the dust approximation.

Abstract: The WiggleZ Dark Energy Survey is a large-scale structure survey of intermediate-redshift ultraviolet-selected (UV-selected) emission-line galaxies scheduled to cover 1000 deg(2), spanning a broad redshift range 0.2 < z < 1.0. The main scientific goal of the survey is the measurement of baryon acoustic oscillations (BAO) in the galaxy clustering pattern at a significantly higher redshift than previous studies. The BAO may be applied as a standard cosmological ruler to constrain dark energy models. Based on the first 20 per cent of the data set, we present initial results concerning the small-scale clustering of the WiggleZ targets, together with survey forecasts. The WiggleZ galaxy population possesses a clustering length r(0) = 4.40 +/- 0.12 h(-1) Mpc, which is significantly larger than z = 0 UV-selected samples, with a slope gamma = 1.92 +/- 0.08. This clustering length is comparable to z = 3 Lyman-break galaxies with similar UV luminosities. The clustering strength of the sample increases with optical luminosity, UV luminosity and reddening rest-frame colour. The full survey, scheduled for completion in 2010, will map an effective volume V(eff) approximate to 1 Gpc(3) (evaluated at a scale k = 0.15 h Mpc(-1)) and will measure the angular diameter distance and Hubble expansion rates in three redshift bins with accuracies of approximate to 5 per cent. We will determine the value of a constant dark energy equation-of-state parameter, w(cons), with a higher precision than existing supernovae observations using an entirely independent technique. The WiggleZ and supernova measurements lie in highly complementary directions in the plane of w(cons) and the matter density Omega(m). The forecast using the full combination of WiggleZ, supernova and cosmic microwave background (CMB) data sets is a marginalized error Delta w(cons) = 0.07, providing a robust and precise measurement of the properties of dark energy including cross-checking of systematic errors.

Abstract: The plethora of recent cosmologically relevant data has indicated that our Universe is very well fitted by a standard Friedmann-Lemaitre-Robertson-Walker (FLRW) model, with Ω M ≈ 0.27 and Ω Λ ≈ 0.73 - or, more generally, by nearly flat FLRW models with parameters close to these values. Additional independent cosmological information, particularly the maximum of the angular-diameter (observer area) distance and the redshift at which it occurs, would improve and confirm these results, once sufficient precise Type Ia supernovae data in the range 1.5 < z < 1.8 become available. We obtain characteristic FLRW-closed functional forms for C = C(z) and M 0 = M 0 (z), the angular-diameter distance and the density per source counted, respectively, when A ≠ 0, analogous to those we have for A = 0. More importantly, we verify that for flat FLRW models z max - as is already known but rarely recognized - the redshift of C max , the maximum of the angular-diameter distance, uniquely gives Ω Λ , the amount of vacuum energy in the universe, independent of H 0 , the Hubble parameter. For non-flat models, determination of both z max and C max gives both Ω Λ and Ω M , the amount of matter in the universe, as long as we know H 0 independently. Finally, determination of C max automatically gives a very simple observational criterion for whether or not the universe is flat - presuming that it is FLRW.

Abstract: Scaling relations among galaxy cluster observables, which will become available in large future samples of galaxy clusters, could be used to constrain not only cluster structure, but also cosmology. We study the utility of this approach, employing a physically motivated parametric model to describe cluster structure, and applying it to the expected relation between the Sunyaev-Zel'dovich decrement (S_ u) and the emission-weighted X-ray temperature (T_ew). The slope and normalization of the entropy profile, the concentration of the dark matter potential, the pressure at the virial radius, and the level of non-thermal pressure support, as well as the mass and redshift-dependence of these quantities are described by free parameters. With a suitable choice of fiducial parameter values, the cluster model satisfies several existing observational constraints. We employ a Fisher matrix approach to estimate the joint errors on cosmological and cluster structure parameters from a measurement of S_ u vs. T_ew in a future survey. We find that different cosmological parameters affect the scaling relation differently: predominantly through the baryon fraction (\Omega_m and \Omega_b), the virial overdensity (w_0 and w_a for low-z clusters) and the angular diameter distance (w_0, w_a for high-z clusters; \Omega_DE and h). We find that the cosmology constraints from the scaling relation are comparable to those expected from the number counts (dN/dz) of the same clusters. The scaling relation approach is relatively insensitive to selection effects and it offers a valuable consistency check; combining the information from the scaling relation and dN/dz is also useful to break parameter degeneracies and help disentangle cluster physics from cosmology.

Abstract: Forthcoming photometric redshift surveys should provide an accurate probe of the acoustic peak in the two-point galaxy correlation function, in the form of angular clustering of galaxies within a given shell in redshift space. We investigate the form of the anticipated signal, quantifying the distortions that arise due to projection effects, and, in particular, explore the validity of applying the Limber approximation. A single-integral prescription is presented, which provides an alternative to Limber's equation, and produces a significantly improved prediction in the regime of interest. The position of the acoustic peak within the angular correlation function relates to the angular diameter distance to the far side of the redshift bin. Thicker redshift bins therefore shift comoving features toward smaller angular scales. As a result, the value of the photometric redshift error acquires a greater significance, particularly at lower redshifts. In order to recover the dark energy equation of state to a level of 1 %, we find the total redshift dispersion must be determined to within Δ σz ≤ 10 -3 , which may prove challenging to achieve in practice.

Abstract: We derive an expression for the luminosity distance as a function of redshift for a flat Robertson-Walker spacetime perturbed by arbitrary scalar perturbations possibly produced by a modified gravity theory with two different scalar perturbation potentials. Measurements of the luminosity distance as function of redshift provide a constraint on a combination of the scalar potentials and so they can complement weak lensing and other measurements in trying to distinguish among the various alternative theories of gravity.

Abstract: We derive an expression for the luminosity distance as a function of redshift for a flat Robertson-Walker spacetime perturbed by arbitrary scalar perturbations possibly produced by a modified gravity theory with two different scalar perturbation potentials. Measurements of the luminosity distance as function of redshift provide a constraint on a combination of the scalar potentials and so they can complement weak lensing and other measurements in trying to distinguish among the various alternative theories of gravity.

Abstract: In 2006, we proposed to NASA a detailed concept study of ADEPT (the Advanced Dark Energy Physics Telescope), a potential space mission to reliably measure the time-evolution of dark energy by conducting the largest effective volume survey of the universe ever done A peer-review panel of scientific, management, and technical experts reported back the highest possible 'excellent' rating for ADEPT We have since made substantial advances in the scientific and technical maturity of the mission design With this Department of Energy (DOE) award we were granted supplemental funding to support specific extended research items that were not included in the NASA proposal, many of which were intended to broadly advance future dark energy research, as laid out by the Dark Energy Task Force (DETF) The proposed work had three targets: (1) the adaptation of large-format infrared arrays to a 2 micron cut-off; (2) analytical research to improve the understanding of the dark energy figure-of- merit; and (3) extended studies of baryon acoustic oscillation systematic uncertainties Since the actual award was only for {approx}10% of the proposed amount item (1) was dropped and item (2) work was severely restricted, consistent with the referee reviews of the proposal, although there was considerablemore » contradictions between reviewer comments and several comments that displayed a lack of familiarity with the research None the less, item (3) was the focus of the work To characterize the nature of the dark energy, ADEPT is designed to observe baryon acoustic oscillations (BAO) in a large galaxy redshift survey and to obtain substantial numbers of high-redshift Type Ia supernovae (SNe Ia) The 2003 Wilkinson Microwave Anisotropy Probe (WMAP) made a precise determination of the BAO 'standard ruler' scale, as it was imprinted on the cosmic microwave background (CMB) at z {approx} 1090 The standard ruler was also imprinted on the pattern of galaxies, and was first detected in 2005 in Sloan Digital Sky Survey (SDSS) data A measurement of the BAO standard ruler as a function of time (or redshift) would provide powerful and reliable observational data to shed light on dark energy In particular, the BAO data provide the angular diameter distance to each redshift, and directly give the expansion rate, H(z), at each redshift The SNe measurements provide luminosity distances A space mission is required to obtain the three-dimensional position of enormous numbers of galaxies at high redshift As recognized by the Dark Energy Task Force, BAO systematic errors are naturally low The following are the key findings: (1) The BAO method is robust (2) Separation of the spectral and imaging detection focal planes vastly improves spectral identifications (3) Prisms instead of grisms provide higher throughput and cleaner spectra Prisms are clearly superior (4) Lower prism dispersions improve signal-to-noise but high prism dispersions improve systematic To ensure that the experiment is not systematic limited, a high dispersion should be used (5) Counter-dispersion of the spectra reduces systematic errors on the redshift determination and assists in the reduction of confusion (6) Small rolls are very effective for the reduction of confusion (7) Interlopers can be recognized by a variety of methods, which combine to produce a sufficiently 'clean' survey data set so as not to limit the dark energy results (8) A space mission can measure the BAO signature to the cosmic variance limit, limited only by statistics and not by systematic (9) Density field reconstruction allows for significant BAO accuracy improvements, well beyond that assumed by the Dark Energy Task Force (10) The BAO method is statistically powerful It is more powerful than previously estimated, and far more powerful than high redshift Type 1a supernovae, for which the ultimate distance accuracy is limited by flux calibration accuracy (11) The BAO technique is far simpler than the weak lensing technique and likely to produce more robust dark energy solutions« less

Abstract: By-now photons are the unique universal messengers. Cosmol gica sources like far-away galaxies or quasars are well-known light-emitters. Here we demon strate that the nonlinear electrodynamics (NLED) description of photon propagation through the weak background intergalactic magnetic fields modifies in a fundamental way the cosmologica l redshift,z, that a direct computation within a specific cosmological model can abscribe to a distant source. Independently of the class of NLED Lagrangian, the effective redshift turns o ut t be(1+z)|eff = (1+z) ∆, where ∆≡ (1+Φe)/(1+Φo), with Φ ≡ 8/3(LFF/LF)B, beingLF = dL/dF, LFF = d2L/dF2, the field F ≡ Fαβ Fαβ , andB the magnetic field strength. Thus the effective redshift is a lways much lower than the standard redshift, but it recovers such limit when t NLED correction∆(Φe,Φo) −→ 1. Therefore, once that we do not actually ever observe proper d istances, then one can argue that for a particular redshift the observed luminosity distance of the light-emitting far-away source is different. The observational implications of this peculia r result are discussed.

Abstract: In this paper we generalize the flux ratio method Bailey et al. (2009) to the case of two luminosity indicators and search the optimal luminosity-flux ratio relations on a set of spectra whose phases are around not only the date of bright light but also other time. With these relations, a new method is proposed to constrain the host galaxy extinction of SN Ia and its distance. It is first applied to the low redshift supernovas and then to the high redshift ones. The results of the low redshift supernovas indicate that the flux ratio method can indeed give well constraint on the host galaxy extinction parameter E(B-V), but weaker constraints on R_{V}. The high redshift supernova spectra are processed by the same method as the low redshift ones besides some differences due to their high redshift. Among 16 high redshift supernovas, 15 are fitted very well except 03D1gt. Based on these distances, Hubble diagram is drew and the contents of the Universe are analyzed. It supports an acceleration behavior in the late Universe. Therefore, the flux ratio method can give constraints on the host galaxy extinction and supernova distance independently. We believe, through further studies, it may provide a precise tool to probe the acceleration of the Universe than before.

Abstract: This work aims to determine the feasibility of an assumed cosmological model by means of a detailed analysis of the brightness profiles of distant galaxies. Starting from the theory of Ellis & Perry (1979) connecting the angular diameter distance obtained from a relativistic cosmological model and the detailed photometry of galaxies, we assume the presently most accepted cosmology with Λ ¬ = 0 and seek to predict the brightness profile of a galaxy in a given redshift z . To do so, we have to make assumptions concerning the galactic brightness structure and evolution, assuming a scenario where the specific emitted surface brightness B e ,ν e can be characterized as, B e ,ν e ( r , z ) = B 0 ( z ) J (ν e , z ) f [ r ( z )/ a ( z )]. Here r is the intrinsic galactic radius, ν e the emitted frequency, B 0 ( z ) the central surface brightness, J (ν e , z ) the spectral energy distribution (SED), f [ r ( z )/ a ( z )] characterizes the shape of the surface profile distribution and a ( z ) is the scaling radius. The dependence on z is due to the galactic evolution. As spacetime curvature affects the received surface brightness, the reciprocity theorem (Ellis 1971) allows us to predict the theoretical received surface brightness. So, we are able to compare the theoretical surface brightness with its equivalent observational data already available for high redshift galaxies in order to test the consistency of the assumed cosmological model. The function f [ r ( z )/ a ( z )] is represented in the literature by various different shapes, like the Hubble, Hubble-Oemler and Abell-Mihalas single parameter profiles, characterizing the galactic surface brightness quite well when the disk or bulge dependence is dominant. Sersic and core-Sersic profiles use two or more parameters and reproduce the galactic profile almost exactly (Trujillo et al . 2004). If we consider all wavelengths, the theory tells us that the total intensity is equal to the surface brightness, so the chosen bandwidth should include most of the SED. In order to analyze only the effect of the cosmological model in the surface brightness and minimize evolutionary effects, we assume that there exists a homogeneous class of objects, whose properties are similar in all redshifts, allowing us to carry out comparisons at different values of z . Studying the parameters that affect the galactic evolution, as well as in others geometrical tests, we will be able to infer some possible galaxy evolution which could reproduce a theoretical surface brightness profile, in order to compare with the observational data and reach conclusions about the observational feasibility of the underlying cosmological model.

Abstract: This work aims to determine the feasibility of an assumed cosmological model by means of a detailed analysis of the brightness profiles of distant galaxies. Starting from the theory of Ellis & Perry (1979) connecting the angular diameter distance obtained from a relativistic cosmological model and the detailed photometry of galaxies, we assume the presently most accepted cosmology with Λ ¬ = 0 and seek to predict the brightness profile of a galaxy in a given redshift z . To do so, we have to make assumptions concerning the galactic brightness structure and evolution, assuming a scenario where the specific emitted surface brightness B e ,ν e can be characterized as, B e ,ν e ( r , z ) = B 0 ( z ) J (ν e , z ) f [ r ( z )/ a ( z )]. Here r is the intrinsic galactic radius, ν e the emitted frequency, B 0 ( z ) the central surface brightness, J (ν e , z ) the spectral energy distribution (SED), f [ r ( z )/ a ( z )] characterizes the shape of the surface profile distribution and a ( z ) is the scaling radius. The dependence on z is due to the galactic evolution. As spacetime curvature affects the received surface brightness, the reciprocity theorem (Ellis 1971) allows us to predict the theoretical received surface brightness. So, we are able to compare the theoretical surface brightness with its equivalent observational data already available for high redshift galaxies in order to test the consistency of the assumed cosmological model. The function f [ r ( z )/ a ( z )] is represented in the literature by various different shapes, like the Hubble, Hubble-Oemler and Abell-Mihalas single parameter profiles, characterizing the galactic surface brightness quite well when the disk or bulge dependence is dominant. Sersic and core-Sersic profiles use two or more parameters and reproduce the galactic profile almost exactly (Trujillo et al . 2004). If we consider all wavelengths, the theory tells us that the total intensity is equal to the surface brightness, so the chosen bandwidth should include most of the SED. In order to analyze only the effect of the cosmological model in the surface brightness and minimize evolutionary effects, we assume that there exists a homogeneous class of objects, whose properties are similar in all redshifts, allowing us to carry out comparisons at different values of z . Studying the parameters that affect the galactic evolution, as well as in others geometrical tests, we will be able to infer some possible galaxy evolution which could reproduce a theoretical surface brightness profile, in order to compare with the observational data and reach conclusions about the observational feasibility of the underlying cosmological model.

Abstract: Scaling relations among galaxy cluster observables, which will become available in large future samples of galaxy clusters, could be used to constrain not only cluster structure, but also cosmology. We study the utility of this approach, employing a physically motivated parametric model to describe cluster structure and applying it to the expected relation between the Sunyaev-Zel'dovich decrement (S v ) and the emission-weighted X-ray temperature (T eW ). The slope and normalization of the entropy profile, the concentration of the dark matter potential, the pressure at the virial radius and the level of non-thermal pressure support as well as the mass and redshift dependence of these quantities are described by free parameters. With a suitable choice of fiducial parameter values, the cluster model satisfies several existing observational constraints. We employ a Fisher matrix approach to estimate the joint errors on cosmological and cluster structure parameters from a measurement of S v versus T ew in a future survey. We find that different cosmological parameters affect the scaling relation differently: predominantly through the baryon fraction (Ω m and Ω b ), the virial overdensity (w 0 and w a for low-z clusters) and the angular diameter distance (w 0 and w a for high-z clusters; Ω DE and h). We find that the cosmology constraints from the scaling relation are comparable to those expected from the number counts (dN/dz) of the same clusters. The scaling-relation approach is relatively insensitive to selection effects and it offers a valuable consistency check; combining the information from the scaling relation and dN/dz is also useful to break parameter degeneracies and help disentangle cluster physics from cosmology. Our work suggests that scaling relations should be a useful component in extracting cosmological information from large future cluster surveys.

Abstract: We show that a cosmic standard ruler can be constructed from the joint measurement of the time delay, , between gravitationally lensed quasar images and the velocity dispersion, σ , of the lensing galaxy. This is specifically shown, for a singular isothermal sphere lens, , where D OL is the angular diameter distance to the lens. Using MCMC simulations we illustrate the constraints set in the plane from future observations.

Abstract: We derive the redshift and the angular diameter distance in rotationless dust universes which are statistically homogeneous and isotropic, but have otherwise arbitrary geometry. The calculation from first principles shows that the Dyer-Roeder approximation does not correctly describe the effect of clumping. Instead, the redshift and the distance are determined by the average expansion rate, the matter density today and the null geodesic shear. In particular, the position of the CMB peaks is consistent with significant spatial curvature provided the expansion history is sufficiently close to the spatially flat ΛCDM model.

Abstract: Conservation of the phase-space density of photons plus Lorentz invariance requires that the cosmological luminosity distance be larger than the angular diameter distance by a factor of (1 + z){sup 2}, where z is the redshift. Because this is a fundamental symmetry, this prediction-known sometimes as the 'Etherington relation' or the 'Tolman test'-is independent of the world model, or even the assumptions of homogeneity and isotropy. It depends, however, on Lorentz invariance and transparency. Transparency can be affected by intergalactic dust or interactions between photons and the dark sector. Baryon acoustic feature (BAF) and type Ia supernovae (SNeIa) measures of the expansion history are differently sensitive to the angular diameter and luminosity distances and can therefore be used in conjunction to limit cosmic transparency. At the present day, the comparison only limits the change {delta}{tau} in the optical depth from redshift 0.20 to 0.35 at visible wavelengths to {delta}{tau} < 0.13 at 95% confidence. In a model with a constant comoving number density n of scatterers of constant proper cross section {sigma}, this limit implies n{sigma} < 2 x 10{sup -4} h Mpc{sup -1}. These limits depend weakly on the cosmological world model. Assuming a concordance world model, the best-fitmore » value of {delta}{tau} to current data is negative at the 2{sigma} level. This could signal interesting new physics or could be the result of unidentified systematics in the BAF/SNeIa measurements. Within the next few years, the limits on transparency could extend to redshifts z {approx} 2.5 and improve to n{sigma} < 1.1 x 10{sup -5} h Mpc{sup -1}. Cosmic variance will eventually limit the sensitivity of any test using the BAF at the n{sigma} {approx} 4 x 10{sup -7} h Mpc{sup -1} level. Comparison with other measures of the transparency is provided; no other measure in the visible is as free of astrophysical assumptions.« less

Abstract: Baryon acoustic oscillations (BAOs) and weak lensing (WL) are complementary probes of cosmology. We explore the distance and growth factor measurements from photometric BAO and WL techniques, and investigate the roles of the distance and growth factor in constraining dark energy. We find for WL that the growth factor has a great impact on dark energy constraints, but is much less powerful than the distance. Dark energy constraints from WL are concentrated in considerably fewer distance eigenmodes than those from BAO, with the largest contributions from modes that are sensitive to the absolute distance. Both techniques have some well-determined distance eigenmodes that are not very sensitive to the dark energy equation-of-state parameters w0 and wa, suggesting that they can accommodate additional parameters for dark energy and for the control of systematic uncertainties. A joint analysis of BAO and WL is far more powerful than either technique alone, and the resulting constraints on the distance and growth factor will be useful for distinguishing dark energy and modified gravity models. The Large Synoptic Survey Telescope (LSST) will yield both WL and angular BAO over a sample of several billion galaxies. Joint LSST BAO and WL can yield 0.5% level precision on ten comoving distances evenly spaced in log(1 + z) between redshift 0.3 and 3 with cosmic microwave background priors from Planck. In addition, since the angular diameter distance, which directly affects the observables, is linked to the comoving distance solely by the curvature radius in the Friedmann-Robertson-Walker metric solution, the LSST can achieve a pure metric constraint of 0.017 on the mean curvature parameter Ω k of the universe simultaneously with the constraints on the comoving distances.

Abstract: We investigate the distance-redshift relation in a realistic inhomogeneous universe where the mass distribution is described by the mass function of Sheth and Tormen. It is found that the derived distance deviates systematically from the standard distance up to 10% depending on the choice of the lowest halo mass in which baryonic matter condensed to form luminous object such as galaxies. Remarkably the derived distance is well approximated by the Dyer-Roeder distance if we choose the clumpiness parameter \alpha calculated by our model.We also discuss the effect of inhomogeneities in the determination of dark energy parameter in the supernovae observation, and find that this effect must be taken into account for the future high redshift supernovae observation.

Abstract: Geometrical tests such as the combination of the Hubble parameter H(z) and the angular diameter distance d_A(z) can, in principle, break the degeneracy between the dark energy equation of state parameter w(z), and the spatial curvature Omega_k in a direct, model-independent way In practice, constraints on these quantities achievable from realistic experiments, such as those to be provided by Baryon Acoustic Oscillation (BAO) galaxy surveys in combination with CMB data, can resolve the cosmic confusion between the dark energy equation of state parameter and curvature only statistically and within a parameterized model for w(z) Combining measurements of both H(z) and d_A(z) up to sufficiently high redshifts around z = 2 and employing a parameterization of the redshift evolution of the dark energy equation of state are the keys to resolve the w(z)-Omega_k degeneracy

Abstract: Lema\^itre - Tolman (L--T) toy models with a central observer have been used to study the effect of large scale inhomogeneities on the SN Ia dimming. Claims that a giant void is mandatory to explain away dark energy in this framework are currently dominating. Our aim is to show that L-T models exist that reproduce a few features of the $\Lambda$CDM model, but do not contain the giant cosmic void. We propose to use two sets of data - the angular diameter distance together with the redshift-space mass-density and the angular diameter distance together with the expansion rate - both defined on the past null cone as functions of the redshift. We assume that these functions are of the same form as in the $\Lambda$CDM model. Using the Mustapha-Hellaby-Ellis algorithm, we numerically transform these initial data into the usual two L-T arbitrary functions and solve the evolution equation to calculate the mass distribution in spacetime. For both models, we find that the current density profile does not exhibit a giant void, but rather a giant hump. However, this hump is not directly observable, since it is in a spacelike relation to a present observer. The alleged existence of the giant void was a consequence of the L-T models used earlier because their generality was limited a priori by needless simplifying assumptions, like, for example, the bang-time function being constant. Instead, one can feed any mass distribution or expansion rate history on the past light cone as initial data to the L-T evolution equation. When a fully general L-T metric is used, the giant void is not implied.