Formula omitted] quantum corrected scalar field inflation

In this paper, we make a detailed side-by-side comparison between Jordan and Einstein frames in the context of cosmic magnetogenesis. We have computed the evolution of the vector potential in each frame along with some observables such as the spectral index and the magnetic field amplitude. We found that contrary to the Einstein frame, the electric and magnetic energy densities in the Jordan Frame do not depend on any parameter associated with the scalar field. Furthermore, in the Einstein frame, and assuming scale invariance for the magnetic field, most of the total energy density contribution comes from the electric and magnetic densities. Finally, we show the ratio between magnetic field signals in both frames printed in the CMB.

We revisit the problem of generality of Starobinsky and Higgs inflation. The known results obtained in the Einstein frame are generalized for the case of an arbitrary initial energy of the scalar field. These results are compared with the results obtained directly in the Jordan frame, which, to our knowledge, has not been thoroughly explored in the literature previously. We demonstrate that the qualitative picture of initial conditions zone in the $(\ensuremath{\phi},\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\phi}})$ plane, which leads to sufficient amount of inflation, is quite similar for both the frames in the case of Higgs inflation. For Starobinsky inflation, the conformal transformation between the frames relates the geometrical variables in the Jordan frame with the properties of an effective scalar field in the Einstein frame. We show that the transformation $(H,R)\ensuremath{\rightarrow}(\ensuremath{\phi},\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\phi}})$ is not regular everywhere, leading to some peculiarities in the zone of good initial conditions in the $(H,R)$ plane.

The unification of quantum principles with Einstein's geometric conception of spacetime and gravity into a consistent theory of quantum gravity is one of the main open challenges at the foundations of modern theoretical physics. Among several approaches developed over the years, the two main candidates are string theory and loop quantum gravity (LQG). Both theories are characterized by their own achievements and open issues so that the solution to the problem of quantum gravity remains still elusive. In lack of experimental guidance, in order to make progress, it becomes important to single out common features shared by different approaches allowing to merge tools and ideas, thus providing indirect tests to potentially overcome current limitations. In this respect, one of the major recent developments is the so-called holographic principle and its string theory-based realization within the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, a conjectured duality between string theory in asymptotically AdS spacetime and a SU(N) gauge theory thought of as living on its conformal boundary. As such it provides a promising arena to look for possible connections between non-perturbative LQG and string theory non-perturbatively defined via its dual field theory. With this motivation in mind, in this thesis we focus on effective symmetry-reduced models for resolved cosmological and black hole singularities to which lot of effort has been devoted within the LQG community and their possible embedding within the AdS/CFT framework. First of all, we focus on the field theory signatures of the singularity resolution in the bulk of Kasner-AdS spacetimes and show via several examples of quantum corrected effective geometries that the finite-distance pole in the boundary two-point correlator previously interpreted as the holographic signature of the bulk singularity is smoothed out by quantum gravity effects. The time dependence of the boundary spacetime however prevents us from setting up an independent field theory computation to compare with the bulk gravity results. We move then to black hole (BH) singularities whose asymptotic boundary is Minkowski or AdS. Since no fully satisfactory effective LQG model is available already for the simplest static spherically symmetric case with zero cosmological constant, we consider the case of a 4-dimensional Schwarzschild BH as a necessary preparation for higher dimensional extensions to AdS BHs. New models based on new sets of canonical variables directly related to the Kretschmann scalar are thus introduced to take the onset of quantum effects under control, and the resulting quantum corrected spacetime structure is discussed in detail. A key ingredient of our analysis is the study of Dirac observables for the asymptotic ADM masses and their relation with admissible initial conditions for the effective dynamics compatibly with the requirement of a unique upper bound on curvature invariants resolving the central singularity. Finally, quantum corrections to thermodynamic quantities are also analyzed and, coming back to the original motivation of using LQG techniques for AdS/CFT, a possible extension to arbitrary dimensions and negative cosmological constant is sketched.

In this note we consider the issue of the classical equivalence of scale-invariant gravity in the Einstein and in the Jordan frames. We first consider the simplest example $f(R)=R^{2}$ and show explicitly that the equivalence breaks down when dealing with Ricci-flat solutions. We discuss the link with the fact that flat solutions in quadratic gravity have zero energy. We also consider the case of scale-invariant tensor-scalar gravity and general $f(R)$ theories. We argue that all scale-invariant gravity models have Ricci flat solutions in the Jordan frame that cannot be mapped into the Einstein frame. In particular, the Minkowski metric exists only in the Jordan frame. In this sense, the two frames are not equivalent.

There are several approaches to quantum gravitational corrections of black hole thermodynamics. String theory and loop quantum gravity, by direct analysis on the basis of quantum properties of black holes, show that in the entropy–area relation the leading order correction should be of log-area type. On the other hand, generalized uncertainty principle (GUP) and modified dispersion relations (MDRs) provide perturbational framework for such modifications. Although both GUP and MDRs are common features of all quantum gravity scenarios, their functional forms are quantum gravity model dependent. Since both string theory and loop quantum gravity give more reliable solution of the black hole thermodynamics, one can use their results to test approximate results of GUP and MDRs. In this Letter, we find quantum corrected black hole thermodynamics in the framework of GUP and MDR and then we compare our results with string theory solutions. This comparison suggests severe constraints on the functional form of GUP and MDRs. These constraints may reflect characteristic features of ultimate quantum gravity theory.

We will summarize recent results on the Hamiltonian equivalence between the Jordan and Einstein frames based on the analysis of Brans-Dicke theory for both cases ω ≠ − 3 2 and ω = − 3 2 We will introduce and perform ADM analysis for spherically symmetric solutions of gravity. We will discuss with particular care the problem of the boundary terms to be introduced in the general case of spherical symmetry. These two frames are connected through a Hamiltonian canonical transformation on the reduced phase space obtained by gauge fixing the lapse and the radial shift functions. We introduce and discuss two static solutions (Fisher, Janis, Newman and Winicour solution in the Einstein frame and Bocharova-Bronnikov-Melnikov-Bekenstein black hole solution in the Jordan frame)

In this talk, we presented the null geodesics of the static charged black hole in heterotic string theory. The talk is based on a paper published in Physical Review D (Fernando, Phys. Rev. D 85:02403, 2012). In this paper, a detailed analysis of the geodesics are done in the Einstein frame as well as in the string frame. In the Einstein frame, the geodesics are solved exactly in terms of the Jacobi-elliptic integrals for all possible energy levels and angular momentum of the photons. In the string frame, the geodesics are presented for the circular orbits. As a physical application of the null geodesics, we have obtained the angle of deflection for the photons and the quasinormal modes of a massless scalar field in the eikonal limit.

We present a critical discussion of quantum corrections,renormalisation, and the computation of the beta functions and theeffective potential in Higgs inflation. In contrast with claims inthe literature, we find no evidence for a disagreement between theJordan and Einstein frames, even at the quantum level. For clarity ofdiscussion we concentrate on the case of a real scalar Higgs. Wefirst review the classical calculation and then discuss the backreaction of gravity. We compute the beta functions for the Higgsquartic coupling and non-minimal coupling constant. Here, themid-field regime is non-renormalisable, but we are able to give anupper bound on the 1-loop corrections to the effective potential. Weshow that, in computing the effective potential, the Jordan andEinstein frames are compatible if all mass scales are transformedbetween the two frames. As such, it is consistent to take a constantcutoff in either the Jordan or Einstein frame, and both prescriptionsyield the same result for the effective potential. Our results areextended to the case of a complex scalar Higgs.

We review the conformal equivalence in describing the background expansion of the universe by [Formula: see text] gravity both in the Jordan frame and the Einstein frame. In the Jordan frame, we present the general analytic expression for [Formula: see text] models that have the same expansion history as the [Formula: see text]CDM model. This analytic form can provide further insights on how cosmology can be used to test the [Formula: see text] gravity at the largest scales. Moreover we present a systematic and self-consistent way to construct the viable [Formula: see text] model in Jordan frame using the mass dilation rate function from the Einstein frame through the conformal transformation. In addition, we extend our study to the linear perturbation theories and we further exhibit the equivalence of the [Formula: see text] gravity presented in the Jordan frame and Einstein frame in the perturbed space–time. We argue that this equivalence has solid physics root.

In the framework of a general scalar-tensor theory, we investigate the equivalence between two different parametrizations of fields that are commonly used in cosmology - the so-called Jordan frame and Einstein frame. While it is clear that both parametrizations are mathematically equivalent at the level of the classical action, the question about their mathematical equivalence at the quantum level as well as their physical equivalence is still a matter of debate in cosmology. We analyze whether the mathematical equivalence still holds when the first quantum corrections are taken into account. We explicitly calculate the one-loop divergences in both parametrizations by using the generalized Schwinger-DeWitt algorithm and compare both results. We find that the quantum corrections do not coincide off shell and hence induce an off shell dependence on the parametrization. According to the equivalence theorem, the one-loop divergences should however coincide on shell. For a cosmological background, we show explicitly that the on shell equivalence is indeed realized by a nontrivial cancellation.

We consider a general scalar-tensor theory of gravity and review briefly different forms it can be presented (different conformal frames and scalar field parametrizations). We investigate the conditions under which its field equations and the parametrized post-Newtonian parameters coincide with those of general relativity. We demonstrate that these so-called limits of general relativity are independent of the parametrization of the scalar field, although the transformation between scalar fields may be singular at the corresponding value of the scalar field. In particular, the limit of general relativity can equivalently be determined and investigated in the commonly used Jordan and Einstein frames.

Quantum corrections to slow roll inflation and new scaling of superhorizon fluctuations

This is a short review of string cosmology. We wish to connect string-scale physics as closely as possible to observables accessible to current or near-future experiments. Our possible best hope to do so is a description of inflation in string theory. The energy scale of inflation can be as high as that of Grand Unification (GUT). If this is the case, this is the closest we can possibly get in energy scales to string-scale physics. Hence, GUT-scale inflation may be our best candidate phenomenon to preserve traces of string-scale dynamics. Our chance to look for such traces is the primordial gravitational wave, or tensor mode signal produced during inflation. For GUT-scale inflation this is strong enough to be potentially visible as a B-mode polarization of the cosmic microwave background (CMB). Moreover, a GUT-scale inflation model has a trans-Planckian excursion of the inflaton scalar field during the observable amount of inflation. Such large-field models of inflation have a clear need for symmetry protection against quantum corrections. This makes them ideal candidates for a description in a candidate fundamental theory like string theory. At the same time the need of large-field inflation models for UV completion makes them particularly susceptible to preserve imprints of their string-scale dynamics in the inflationary observables, the spectral index ns and the fractional tensor mode power r. Hence, we will focus this review on axion monodromy inflation as a mechanism of large-field inflation in string theory.

Due to the quasi-exponential red-shifting which occurs during an inflationary period in the very early Universe, wavelengths which at the present time correspond to cosmological lengths are in general sub-Planckian during the early stages of inflation. This talk discusses two approaches to addressing this issue which both indicate that the standard predictions of inflationary cosmology - made using classical general relativity and weakly coupled scalar matter field theory - are not robust against changes in the physics on trans-Planckian scales. One approach makes use of modified dispersion relations for a usual free field scalar matter theory, the other uses some properties of space-time non-commutativity - a feature expected in string theory. Thus, it is possible that cosmological observations may be used as a window to explore trans-Planckian physics. We also speculate on a novel way of obtaining inflation based on modified dispersion relations for ordinary radiation.

We discuss wormhole solution in the Brans-Dicke theory with existence of relativistic radiation field. The solutions of wormhole are obtained in the Einstein frame. When the dilaton field σ = const, the solution of wormhole should be reduced to the well-known Tolman wormhole. Euclidean wormhole solution also has been obtained in the Einstein frame when σ ≠ const. For the comparison, we also derive the wormhole solution in the Jordan frame with existence of relativistic radiation field. However, the two frames, the Einstein frame and the Jordan frame, are not physically equivalent.