Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userViable tensor-to-scalar ratio in a symmetric matter bounce
109
0
0.0
(
0
)
Added by
Rathul Nath Raveendran
Publication date
2017
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Matter bounces refer to scenarios wherein the universe contracts at early times as in a matter dominated epoch until the scale factor reaches a minimum, after which it starts expanding. While such scenarios are known to lead to scale invariant spectra of primordial perturbations after the bounce, the challenge has been to construct completely symmetric bounces that lead to a tensor-to-scalar ratio which is small enough to be consistent with the recent cosmological data. In this work, we construct a model involving two scalar fields (a canonical field and a non-canonical ghost field) to drive the symmetric matter bounce and study the evolution of the scalar perturbations in the model. If we consider the scale associated with the bounce to be of the order of the Planck scale, the model is completely described in terms of only one parameter, viz the value of the scale factor at the bounce. We evolve the scalar perturbations numerically across the bounce and evaluate the scalar power spectra after the bounce. We show that, while the scalar and tensor perturbation spectra are scale invariant over scales of cosmological interest, the tensor-to-scalar ratio proves to be much smaller than the current upper bound from the observations of the cosmic microwave background anisotropies by the Planck mission. We also support our numerical analysis with analytical arguments.
rate research
Read More
We study the bounce and cyclicity realization in the framework of new gravitational scalar-tensor theories. In these theories the Lagrangian contains the Ricci scalar and its first and second derivatives, in a specific combination that makes them free of ghosts, and transformed into the Einstein frame they are proved to be a subclass of bi-scalar extensions of general relativity. We present analytical expressions for the bounce requirements, and we examine the necessary qualitative behavior of the involved functions that can give rise to a given scale factor. Having in mind these qualitative forms, we reverse the procedure and we construct suitable simple Lagrangian functions that can give rise to a bounce or cyclic scale factor.
In a recent work, we had constructed a model consisting of two fields---a canonical scalar field and a non-canonical ghost field---that had sourced a symmetric matter bounce scenario. The model had involved only one parameter, viz. the scale associated with the bounce. For a suitable value of the parameter, the model had led to strictly scale invariant power spectra with a COBE normalized scalar amplitude and a rather small tensor-to-scalar ratio. In this work, we extend the model to achieve near-matter bounces, which contain a second parameter apart from the bounce scale. As the new model does not seem to permit analytical evaluation of the scalar modes near the bounce, with the aid of techniques which we had used in our earlier work, we compute the scalar and the tensor power spectra numerically. For appropriate values of the additional parameter, we find that the model produces red spectra with a scalar spectral tilt and a small tensor-to-scalar ratio which are consistent with the recent observations of the anisotropies in the cosmic microwave background by Planck.
The scalar-tensor theory can be formulated in both Jordan and Einstein frames, which are conformally related together with a redefinition of the scalar field. As the solution to the equation of the scalar field in the Jordan frame does not have the one-to-one correspondence with that in the Einstein frame, we give a criterion along with some specific models to check if the scalar field in the Einstein frame is viable or not by confirming whether this field is reversible back to the Jordan frame. We further show that the criterion in the first parameterized post-Newtonian approximation can be determined by the parameters of the osculating approximation of the coupling function in the Einstein frame and can be treated as a viable constraint on any numerical study in the scalar-tensor scenario. We also demonstrate that the Brans-Dicke theory with an infinite constant parameter $omega_{text{BD}}$ is a counterexample of the equivalence between two conformal frames due to the violation of the viable constraint.
In this work we shall demonstrate that it is possible to describe in a unified way a primordial bounce with the dark energy era, in the context of Gauss-Bonnet modified gravity. Particularly, the early time bounce has a nearly scale invariant power spectrum of primordial scalar curvature perturbations, while the dark energy era is a viable one, meaning that it mimics the $Lambda$-Cold-Dark-Matter model and also is compatible with the Planck 2018 data on cosmological parameters. In addition, our analysis indicates that the dark energy era is free from dark energy oscillations, which occur in the context of $f(R)$ gravity. We further addressed the later issue by examining $f(R)$ extensions of Gauss-Bonnet models, and we showed that the $f(R)$ gravity part of the action actually produces the dark energy oscillations at redshifts $zsim 4$.
We study the structure of scalar-tensor theories of gravity based on derivative couplings between the scalar and the matter degrees of freedom introduced through an effective metric. Such interactions are classified by their tensor structure into conformal (scalar), disformal (vector) and extended disformal (traceless tensor), as well as by the derivative order of the scalar field. Relations limited to first derivatives of the field ensure second order equations of motion in the Einstein frame and hence the absence of Ostrogradski ghost degrees of freedom. The existence of a mapping to the Jordan frame is not trivial in the general case, and can be addressed using the Jacobian of the frame transformation through its eigenvalues and eigentensors. These objects also appear in the study of different aspects of such theories, including the metric and field redefinition transformation of the path integral in the quantum mechanical description. Although sane in the Einstein frame, generic disformally coupled theories are described by higher order equations of motion in the Jordan frame. This apparent contradiction is solved by the use of a hidden constraint: the contraction of the metric equations with a Jacobian eigentensor provides a constraint relation for the higher field derivatives, which allows one to express the dynamical equations in a second order form. This signals a loophole in Horndeskis theorem and allows one to enlarge the set of scalar-tensor theories which are Ostrogradski-stable. The transformed Gauss-Bonnet terms are also discussed for the simplest conformal and disformal relations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
