Scalar fields have played an important role in the development of the fundamental theories of physics as well as in other branches of physics such as gravitation and cosmology. For a long time, the...

Selected topics in scalar–tensor theories and beyond

Scalar fields have played an important role in the development of the fundamental theories of physics as well as in other branches of physics such as gravitation and cosmology. For a long time these escaped detection until 2012 year when the Higgs boson was observed for the first time. Since then alternatives to the general theory of relativity like the Brans-Dicke theory, scalar-tensor theories of gravity and their higher derivative generalizations -- collectively known as Horndeski theories -- have acquired renewed interest. In the present review we discuss on several selected topics regarding these theories, mainly from the theoretical perspective but with due mention of the observational aspect. Among the topics covered in this review we pay special attention to the following: 1) the asymptotic dynamics of cosmological models based in the Brans-Dicke, scalar-tensor and Horndeski theories, 2) inflationary models, extended quintessence and the Galileons, with emphasis in causality and stability issues, 3) the chameleon and Vainshtein screening mechanisms that may allow the elusive scalar field to evade the tight observational constraints implied by the solar system experiments, 4) the conformal frames conundrum with a brief discussion on the disformal transformations and 5) the role of Weyl symmetry and scale invariance in the gravitation theories. The review is aimed at specialists as well as at non-specialists in the subject, including postgraduate students.

Selected topics in scalar-tensor theories and beyond

We have studied the Generalised Brans-Dicke theory and obtained exact solutions of a(t),phi(t),and omega(t) for different epochs of the cosmic evolution .We discuss how inflation,decceleration,cosmic acceleration can result from this solution.The time variation of G(t) is also examined.

Cosmic Evolution in Generalised Brans-Dicke Theory

We compute analytically the dominant contribution to the tree-level bispectrum in the Starobinsky model of inflation. In this model, the potential is vacuum energy dominated but contains a subdominant linear term which changes the slope abruptly at a point. We show that on large scales compared with the transition scale k0 and in the equilateral limit the analogue of the non-linearity parameter scales as (k/k0)2, that is its amplitude decays for larger and larger scales until it becomes subdominant with respect to the usual slow-roll suppressed corrections. On small scales we show that the non-linearity parameter oscillates with angular frequency given by 3/k0 and its amplitude grows linearly towards smaller scales and can be large depending on the model parameters. We also compare our results with previous results in the literature.

Strong scale dependent bispectrum in the Starobinsky model of inflation

A characteristic signature of String Gas Cosmology is primordial power spectra for scalar and tensor modes which are almost scale-invariant but with a red tilt for scalar modes but a blue tilt for tensor modes. This feature, however, can also be realized in the so-called G-inflation model, in which Horndeski operators are introduced which leads to a blue tensor tilt by softly breaking the Null Energy Condition. In this article we search for potential observational differences between these two cosmologies by performing detailed perturbation analyses based on the Effective Field Theory approach. Our results show that, although both two models produce blue tilted tensor perturbations, they behave differently in three aspects. Firstly, String Gas Cosmology predicts a specific consistency relation between the index of the scalar modes ns and that of tensor ones nt, which is hard to be reproduced by G-inflation. Secondly, String Gas Cosmology typically predicts non-Gaussianities which are highly suppressed on observable scales, while G-inflation gives rise to observationally large non-Gaussianities because the kinetic terms in the action become important during inflation. However, after finely tuning the model parameters of G-inflation it is possible to obtain a blue tensor spectrum and negligible non-Gaussianities with a degeneracy between the two models. This degeneracy can be broken by a third observable, namely the scale dependence of the nonlinearity parameter, which vanishes for G-inflation but has a blue tilt in the case of String Gas Cosmology. Therefore, we conclude that String Gas Cosmology is in principle observationally distinguishable from the single field inflationary cosmology, even allowing for modifications such as G-inflation.

/pdf/differentiating-g-inflation-from-string-gas-cosmology-using-508atte13x.pdf

Differentiating G-inflation from String Gas Cosmology using the Effective Field Theory Approach

We study FRW cosmology for a double scalar-tensor theory of gravity where two scalar fields are nonminimally coupled to the geometry. In a framework to study stability and attractor solutions of the model in the phase space, we constrain the model parameters with the observational data. For an accelerating universe, the model behaves like quintom dark energy models and predicts a transition from quintessence era to phantom era.

https://www.tpbin.com/Uploads/Subjects/5d0d7d75-52b0-4030-8ce2-155588b25f76.pdf

Dynamical stability in scalar-tensor cosmology

We study FRW cosmology for a double scalar - tensor theory of gravity where two scalar fields are nonminimally coupled to the geometry. In a framework to study stability and attractor solutions of the model in the phase space, we constraint the model parameters with the observational data. For an accelerating universe, the model behaves like quintom dark energy models and predicts a transition from quintessence era to phantom era.

We study the dynamics of the scalar tensor cosmological model in the presence of tachyon field. In an alternative approach, in two exponential and power law form of the scalar field functions in the model, field equations are solved by simultaneously best fitting the model parameters with the most recent observational data. This approach gives us an observationally verified interpretation of the dynamics of the universe. We then discuss the best fitted of equation of state parameter, the statefinder parameters and the reconstructed scalar field in the model.

Observational constraints in scalar tensor theory with tachyonic potential

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Dynamical stability in scalar-tensor cosmology

Dynamical stability in scalar-tensor cosmology

Observational constraints in scalar tensor theory with tachyonic potential