scholarly journals Inflation in f(R,ϕ) Gravity with Exponential Model

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Farzana Kousar ◽  
Rabia Saleem ◽  
M. Zubair
Keyword(s):  
Power Spectra ◽  
Exponential Model ◽  
Jordan Frame ◽  
Spectral Indices ◽  
Nonminimal Coupling ◽  
Tensor Power ◽  
Tensor Theory ◽  
Slow Roll ◽  
Frame Dependence ◽  
Taking Action

We are taking action of f(R) gravity with a nonminimal coupling to a massive inflaton field. A f(R,ϕ) model is chosen which leads to the scalar-tensor theory which can be transformed to Einstein frame by conformal transformation. To avoid the vagueness of the frame dependence, we evaluate the exact analytical solutions for inflationary era in Jordan frame and find a condition for graceful exit from inflation. Furthermore, we calculate the perturbed parameters (i.e., number of e-folds, slow-roll parameters, scalar and tensor power spectra, corresponding spectral indices, and tensor to scalar ratio). It is showed that the tensor power spectra lead to blue tilt for this model. The trajectories of the perturbed parameters are plotted to compare the results with recent observations.

Shaft potential inspired warm inflation

2017 ◽  
Vol 14 (06) ◽  
pp. 1750088 ◽  
Author(s):  
Abdul Jawad ◽  
Amara Ilyas ◽  
Sarfraz Ahmad
Keyword(s):  
Scalar Field ◽  
Spectral Index ◽  
Power Spectra ◽  
Spectral Indices ◽  
Tensor Power ◽  
Planck Data ◽  
Warm Inflation ◽  
Slow Roll ◽  
Scalar Spectral Index ◽  
Inflationary Parameters

We discuss the warm inflation in the presence of shaft potential [Formula: see text], tachyon scalar field and the generalized form of dissipative coefficient [Formula: see text]. In this respect, we investigate the inflationary parameters (slow-roll parameters, number of e-folds, scalar-tensor power spectra, spectral indices, tensor-to-scalar ratio and running of scalar spectral index) in both strong and weak dissipative regimes. It is interesting to mention that our inflationary parametric results (tensor-scalar ratio, spectral index and running of spectral) are consistent with the recent observational data such as BICEP[Formula: see text], WMAP[Formula: see text] and latest Planck data.

scholarly journals Inflationary perturbation spectra at next-to-leading slow-roll order in effective field theory of inflation

2019 ◽  
Vol 79 (11) ◽  
Author(s):  
Guang-Hua Ding ◽  
Jin Qiao ◽  
Qiang Wu ◽  
Tao Zhu ◽  
Anzhong Wang
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
High Energy Physics ◽  
Power Spectra ◽  
High Energy ◽  
Effective Field ◽  
Spectral Indices ◽  
Leading Order ◽  
Slow Roll ◽  
Tensor Perturbations

AbstractThe effective field theory (EFT) of inflation provides an essential picture to explore the effects of the unknown high energy physics in the single scalar field inflation models. For a generic EFT of inflation, possible high energy corrections to simple slow-roll inflation can modify both the propagating speed and dispersion relations of the cosmological scalar and tensor perturbations. With the arrival of the era of precision cosmology, it is expected that these high energy corrections become more important and have to be taken into account in the analysis with future precise observational data. In this paper we study the observational predictions of the EFT of inflation by using the third-order uniform asymptotic approximation method. We calculate explicitly the primordial power spectra, spectral indices, running of the spectral indices for both scalar and tensor perturbations, and the ratio between tensor and scalar spectra. These expressions are all written in terms of the Hubble flow parameters and the flow of four new slow-roll parameters and expanded up to the next-to-leading order in the slow-roll expansions so they represent the most accurate results obtained so far in the literature. The flow of the four new slow-roll parameters, which arise from the four new operators introduced in the action of the EFT of inflation, can affect the primordial perturbation spectra at the leading-order and the corresponding spectral indices at the next-to-leading order.

INFLATION AND ACCELERATING UNIVERSE IN MODIFIED MODULAR INVARIANT SUPERGRAVITY

2012 ◽  
Vol 27 (31) ◽  
pp. 1250180
Author(s):  
TOYOKAZU FUKUOKA ◽  
YUTA KOSHIMIZU ◽  
KENJI TAKAGI ◽  
HIKOYA KASARI ◽  
MITSUO J. HAYASHI
Keyword(s):  
Power Spectra ◽  
Fine Tuning ◽  
Accelerated Expansion ◽  
Wilkinson Microwave Anisotropy Probe ◽  
Accelerating Universe ◽  
Tensor Power ◽  
Modular Invariant ◽  
Slow Roll ◽  
Inflationary Parameters ◽  
The Universe

A method of explaining the recently observed acceleration of cosmic expansion as well as inflation in the early universe is presented within the same framework. The goal is to construct an inflation model based on supergravity and the slow-roll approximation (SRA) that both satisfactorily predicts observed inflationary parameters and at the same time explains the accelerated expansion of the universe. The model is based on a modification of string-based modular invariant supergravity previously proposed by the present authors. It realizes slow-roll inflation in the Einstein frame and is successful in explaining Wilkinson Microwave Anisotropy Probe (WMAP) observational data, through fine-tuning procedure of free parameters. The parameter dependence of the model is considered in detail in order to determine the range for which the SRA can be applied. Within the allowed range of parameter values, a vacuum energy of ~10-120 can be obtained, which coincides with the cosmological constant, and can play the role of dark energy in the universe. The calculated inflationary parameters fit very well to seven-year WMAP data. The ratio of the scalar and tensor power spectra is predicted to be r ~6.8 ×10-2, and this may soon be verified by observations by the Planck satellite. The non-Gaussianity parameter fNL is also estimated by the slow-roll parameters.

On Primordial Black Holes and secondary gravitational waves generated from inflation with solo/multi-bumpy potential

2021 ◽  
Author(s):  
Rui feng Zheng ◽  
Jia ming Shi ◽  
Taotao Qiu
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gravitational Waves ◽  
Power Spectra ◽  
Small Scale ◽  
Primordial Black Hole ◽  
Primordial Black Holes ◽  
Slow Roll ◽  
Spherical Collapse ◽  
Scalar Perturbations

Abstract It is well known that primordial black hole (PBH) can be generated in inflation process of the early universe, especially when the inflaton field has some non-trivial features that could break the slow-roll condition. In this paper, we investigate a toy model of inflation with bumpy potential, which has one or several bumps. We found that potential with multi-bump can give rise to power spectra with multi peaks in small-scale region, which can in turn predict the generation of primordial black holes in various mass ranges. We also consider the two possibilities of PBH formation by spherical collapse and elliptical collapse. And discusses the scalar-induced gravitational waves (SIGWs) generated by the second-order scalar perturbations.

scholarly journals Scalar and tensor perturbations in DHOST bounce cosmology

2021 ◽  
Vol 2021 (11) ◽  
pp. 045
Author(s):  
Mian Zhu ◽  
Amara Ilyas ◽  
Yunlong Zheng ◽  
Yi-Fu Cai ◽  
Emmanuel N. Saridakis
Keyword(s):  
Scale Invariance ◽  
Initial Conditions ◽  
Power Spectra ◽  
Thermal Fluctuations ◽  
Spectral Indices ◽  
Vacuum Fluctuations ◽  
Perfect Agreement ◽  
Expansion Phase ◽  
Contraction Phase ◽  
Tensor Perturbations

Abstract We investigate the bounce realization in the framework of DHOST cosmology, focusing on the relation with observables. We perform a detailed analysis of the scalar and tensor perturbations during the Ekpyrotic contraction phase, the bounce phase, and the fast-roll expansion phase, calculating the power spectra, the spectral indices and the tensor-to-scalar ratio. Furthermore, we study the initial conditions, incorporating perturbations generated by Ekpyrotic vacuum fluctuations, by matter vacuum fluctuations, and by thermal fluctuations. The scale invariance of the scalar power spectrum can be acquired introducing a matter contraction phase before the Ekpyrotic phase, or invoking a thermal gas as the source. The DHOST bounce scenario with cosmological perturbations generated by thermal fluctuations proves to be the most efficient one, and the corresponding predictions are in perfect agreement with observational bounds. Especially the tensor-to-scalar ratio is many orders of magnitude within the allowed region, since it is suppressed by the Hubble parameter at the beginning of the bounce phase.

scholarly journals Viability of slow-roll inflation in light of the non-zero k min measured in the cosmic microwave background power spectrum

2020 ◽  
Vol 476 (2239) ◽  
pp. 20200364
Author(s):  
Jingwei Liu ◽  
Fulvio Melia
Keyword(s):  
Spectral Indices ◽  
Fluctuation Spectrum ◽  
Microwave Background ◽  
Scale Free ◽  
Horizon Problem ◽  
Slow Roll ◽  
Inflationary Phase ◽  
Joint Resolution ◽  
Conventional Picture ◽  
Slow Roll Inflation

Slow-roll inflation may simultaneously solve the horizon problem and generate a near scale-free fluctuation spectrum P ( k ). These two processes are intimately connected via the initiation and duration of the inflationary phase. But a recent study based on the latest Planck release suggests that P ( k ) has a hard cut-off, k min ≠ 0 , inconsistent with this conventional picture. Here, we demonstrate quantitatively that most—perhaps all—slow-roll inflationary models fail to accommodate this minimum cut-off. We show that the small parameter ϵ must be ≳ 0.9 throughout the inflationary period to comply with the data, seriously violating the slow-roll approximation. Models with such an ϵ predict extremely red spectral indices, at odds with the measured value. We also consider extensions to the basic picture (suggested by several earlier workers) by adding a kinetic-dominated or radiation-dominated phase preceding the slow-roll expansion. Our approach differs from previously published treatments principally because we require these modifications not only to fit the measured fluctuation spectrum but also simultaneously to fix the horizon problem. We show, however, that even such measures preclude a joint resolution of the horizon problem and the missing correlations at large angles.

Slow-roll inflation in loop quantum cosmology of scalar–tensor theories of gravity

2015 ◽  
Vol 30 (26) ◽  
pp. 1550127
Author(s):  
Yu Han
Keyword(s):  
Quantum Cosmology ◽  
Field Model ◽  
Equations Of Motion ◽  
Index Formula ◽  
Jordan Frame ◽  
Loop Quantum Cosmology ◽  
Slow Roll ◽  
Scalar Spectral Index ◽  
Theories Of Gravity ◽  
Slow Roll Inflation

The slow-roll inflation of scalar–tensor theories (STTs) of gravity in the context of loop quantum cosmology (LQC) is investigated in this paper. After deriving the effective Hamiltonian, we obtain the semiclassical equations of motion for the background variables in both Jordan frame and Einstein frame of STTs. Then we apply these equations in the slow-roll limit and derive the LQC corrections to the scalar spectral index [Formula: see text] and the tensor-to-scalar ratio [Formula: see text] in the two frames of STTs. Finally, we take two special sectors of STTs as specific examples, namely the Starobinsky model and the non-minimally coupled scalar field model (with the coupling function [Formula: see text] and the potential [Formula: see text]). We derive the detailed expressions of the LQC corrections to [Formula: see text] and [Formula: see text] in terms of the [Formula: see text]-folding number for these two models in both frames.

Is Spacetime Non-metric?

2018 ◽  
Vol 2 (1) ◽  
Author(s):  
Mark D. Roberts
Keyword(s):  
General Relativity ◽  
Higher Dimensions ◽  
Christoffel Symbol ◽  
Einstein Frame ◽  
Jordan Frame ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Extra Information ◽  
Tensor Theory ◽  
Palatini Variation

If one assumes higher dimensions and that dimensional reduction from higher dimensions produces scalar-tensor theory and also that Palatini variation is the correct method of varying scalar-tensor theory then spacetime is nonmetric. Palatini variation of Jordan frame lagrangians gives an equation relating the dilaton to the object of non-metricity and hence the existence of the dilaton implies that the spacetime connection is more general than that given soley by the Christoffel symbol of general relativity. Transferring from Jordan to Einstein frame, which connection, lagrangian, field equations and stress conservation equations occur are discussed: it is found that the Jordan frame has more information, this can be expressed in several ways, the simplest is that the extra information corresponds to the function multiplying the Ricci scalar in the action. The Einstein frame has the advantages that stress conservation implies no currents and that the field equations are easier to work with. This is illustrated by application to Robertson-Walker spacetime.

scholarly journals Decaying Cosmological Constant and the Choice of a Conformal Frame

1999 ◽  
Vol 183 ◽  
pp. 310-310
Author(s):  
Yasunori Fujii
Keyword(s):  
Scalar Field ◽  
Cosmological Constant ◽  
Scalar Tensor Theory ◽  
Nonminimal Coupling ◽  
Tensor Theory ◽  
Theory Of Gravity ◽  
To Come ◽  
Hilbert Action

A solution of the cosomlogical constant problem seems to come from a version of the scalar-tensor theory of gravity, which is characterized by a “nonminimal coupling“ in place of the standard Einstein-Hilbert action, where ɸ is the scalar field while ξ a constant. One then encounters an inherent question never fully answered: How can one single out a right conformai frame?

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