scholarly journals Exact and Slow-Roll Solutions for Exponential Power-Law Inflation Connected with Modified Gravity and Observational Constraints

Universe ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. 199
Author(s):  
Igor Fomin ◽  
Sergey Chervon
Keyword(s):  
Scalar Field ◽  
Power Law ◽  
Hubble Parameter ◽  
Gravity Models ◽  
Observational Constraints ◽  
Slow Roll ◽  
Correct Model ◽  
Scalar Spectral Index ◽  
Wide Range ◽  
Exponential Power

We investigate the ability of the exponential power-law inflation to be a phenomenologically correct model of the early universe. We study General Relativity (GR) scalar cosmology equations in Ivanov–Salopek–Bond (or Hamilton–Jacobi like) representation where the Hubble parameter H is the function of a scalar field ϕ. Such approach admits calculation of the potential for given H(ϕ) and consequently reconstruction of f(R) gravity in parametric form. By this manner the Starobinsky potential and non-minimal Higgs potential (and consequently the corresponding f(R) gravity) were reconstructed using constraints on the model’s parameters. We also consider methods for generalising the obtained solutions to the case of chiral cosmological models and scalar-tensor gravity. Models based on the quadratic relationship between the Hubble parameter and the function of the non-minimal interaction of the scalar field and curvature are also considered. Comparison to observation (PLANCK 2018) data shows that all models under consideration give correct values for the scalar spectral index and tensor-to-scalar ratio under a wide range of exponential-power-law model’s parameters.

scholarly journals Light of Planck-2015 on Noncanonical Inflation

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Kh. Saaidi ◽  
A. Mohammadi ◽  
T. Golanbari
Keyword(s):  
Scalar Field ◽  
Observational Data ◽  
Power Law ◽  
Hubble Parameter ◽  
Field Model ◽  
Kinetic Term ◽  
Inflationary Scenario ◽  
Slow Roll ◽  
Power Law Function ◽  
Free Parameters

Slow-roll inflationary scenario is considered in noncanonical scalar field model supposing a power-law function for kinetic term and using two formalisms. In the first approach, the potential is picked out as a power-law function, that is, the most common approach in studying inflation. Hamilton-Jacobi approach is selected as the second formalism, so that the Hubble parameter is introduced as a function of scalar field instead of the potential. Employing the last observational data, the free parameters of the model are constrained, and the predicted form of the potential and attractor behavior of the model are studied in detail.

Inflationary cosmology for f(R, ϕ) models with different potentials

2017 ◽  
Vol 95 (11) ◽  
pp. 1074-1085 ◽  
Author(s):  
M. Zubair ◽  
Farzana Kousar
Keyword(s):  
Scalar Field ◽  
Equation Of State ◽  
Energy Density ◽  
Cosmological Constant ◽  
Observational Data ◽  
Power Law ◽  
Early Time ◽  
Inflationary Cosmology ◽  
Effective Equation ◽  
Slow Roll

We examine inflation in [Formula: see text] theory, where a scalar field is coupled to gravity. We have constructed [Formula: see text] models using exponential and power law potentials and study inflation for these models, which can support the early-time acceleration with a useful cosmological constant at high curvature. We have calculated the slow-roll parameters, scalar-to-tensor ratio, and spectral index for these models and analyzed them graphically to check the viability according to recent observational data. We have also presented the evolution of effective equation of state and energy density.

scholarly journals Dynamics of tachyon fields and inflation - comparison of analytical and numerical results with observation

2016 ◽  
pp. 1-8 ◽  
Author(s):  
M. Milosevic ◽  
D.D. Dimitrijevic ◽  
G.S. Djordjevic ◽  
M.D. Stojanovic
Keyword(s):  
Scalar Field ◽  
String Theory ◽  
Numerical Methods ◽  
Spectral Index ◽  
Early Universe ◽  
Slow Roll ◽  
Scalar Spectral Index ◽  
Homogeneous Universe ◽  
The Given ◽  
Good Agreement

The role tachyon fields may play in evolution of early universe is discussed in this paper. We consider the evolution of a flat and homogeneous universe governed by a tachyon scalar field with the DBI-type action and calculate the slow-roll parameters of inflation, scalar spectral index (n), and tensor-scalar ratio (r) for the given potentials. We pay special attention to the inverse power potential, first of all to V (x) ~ x?4, and compare the available results obtained by analytical and numerical methods with those obtained by observation. It is shown that the computed values of the observational parameters and the observed ones are in a good agreement for the high values of the constant X0. The possibility that influence of the radion field can extend a range of the acceptable values of the constant X0 to the string theory motivated sector of its values is briefly considered.

scholarly journals WHAT IF THE INFLATON IS A SPINOR CONDENSATE?

2009 ◽  
Vol 18 (14) ◽  
pp. 2173-2179 ◽  
Author(s):  
S. SHANKARANARAYANAN
Keyword(s):  
Scalar Field ◽  
Gravitational Wave ◽  
Spectral Index ◽  
Spinor Condensate ◽  
Slow Roll ◽  
Scalar Spectral Index ◽  
The Future ◽  
Wmap Data ◽  
Elementary Field ◽  
Canonical Scalar Field

In the usual cosmological inflationary scenarios, the scalar field — the inflaton — is usually assumed to be an elementary field. In this essay, we ask: What are the observational signatures if the scalar field is a spinor condensate? And is there a way to distinguish between the canonical scalar field and the spinor-condensate-driven models? In the homogeneous and isotropic background, we show that — although the dark-spinor (Elko) condensate leads to an acceleration equation identical to that of the canonical-scalar-field-driven inflation — the dynamics of the two models are different. In the slow-roll limit, we show that the model predicts a running of the scalar spectral index consistent with the WMAP data. We show that the consistency relations between the spinor condensate and the canonical-scalar-field-driven model are different, which we will be able to test using the future CMB and gravitational wave missions.

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 Nonminimal coupling inflation with constant slow roll

2021 ◽  
pp. 2150070
Author(s):  
Mehdi Shokri ◽  
Jafar Sadeghi ◽  
Mohammad Reza Setare ◽  
Salvatore Capozziello
Keyword(s):  
Scalar Field ◽  
Equations Of Motion ◽  
Nonminimal Coupling ◽  
Coupling Term ◽  
Microwave Background ◽  
First Order ◽  
Slow Roll ◽  
Wide Range ◽  
Single Field ◽  
Inflationary Parameters

In this paper, we study a single-field inflationary model modified by a nonminimal coupling term between the Ricci scalar [Formula: see text] and the scalar field [Formula: see text] in the context of constant-roll inflation. The first-order formalism is used to analyze the constant-roll inflation instead of the standard methods used in the literature. In principle, the formalism considers two functions of the scalar field, [Formula: see text] and [Formula: see text], which lead to the reduction of the equations of motion to first-order differential equations. The approach can be applied to a wide range of cosmological situations since it directly relates the function [Formula: see text] with Hubbles parameter [Formula: see text]. We perform the inflationary analysis for power-law and exponential couplings, separately. Then, we investigate the features of constant-roll potentials as inflationary potentials. Finally, we compare the inflationary parameters of the models with the observations of Cosmic Microwave Background (CMB) anisotropies in view of realizing a physically motivated model.

scholarly journals COSMOLOGICAL DYNAMICS OF f(R) GRAVITY SCALAR DEGREE OF FREEDOM IN EINSTEIN FRAME

2013 ◽  
Vol 22 (14) ◽  
pp. 1350083 ◽  
Author(s):  
UMANANDA DEV GOSWAMI ◽  
KABITA DEKA
Keyword(s):  
Scalar Field ◽  
Power Law ◽  
Einstein Frame ◽  
Degree Of Freedom ◽  
Gravity Models ◽  
Accelerated Expansion ◽  
Power Law Model ◽  
Starobinsky Model ◽  
Expansion Of The Universe ◽  
The Universe

f(R) gravity models belong to an important class of modified gravity models where the late time cosmic accelerated expansion is considered as a manifestation of the large scale modification of the force of gravity. f(R) gravity models can be expressed in terms of a scalar degree of freedom by redefinition of model's variable. The conformal transformation of the action from Jordan frame to Einstein frame makes the scalar degree of freedom more explicit and can be studied conveniently. We have investigated the features of the scalar degree of freedoms and the consequent cosmological implications of the power-law (ξRn) and the Starobinsky (disappearing cosmological constant) f(R) gravity models numerically in the Einstein frame. Both the models show interesting behavior of their scalar degree of freedom and could produce the accelerated expansion of the universe in the Einstein frame with the negative equation of state of the scalar field. However, the scalar field potential for the power-law model is the well-behaved function of the field, whereas the potential becomes flat for higher value of field in the case of the Starobinsky model. Moreover, the equation of state of the scalar field for the power-law model is always negative and less than -1/3, which corresponds to the behavior of the dark energy, that produces the accelerated expansion of the universe. This is not always the case for the Starobinsky model. At late times, the Starobinsky model behaves as cosmological constant Λ as behaves by power-law model for the values of n → 2 at all times.

scholarly journals On f(R) gravity in scalar–tensor theories

2017 ◽  
Vol 14 (07) ◽  
pp. 1750107 ◽  
Author(s):  
Joseph Ntahompagaze ◽  
Amare Abebe ◽  
Manasse Mbonye
Keyword(s):  
Scalar Field ◽  
Gordon Equation ◽  
Gravity Models ◽  
Index Formula ◽  
Coupling Constant ◽  
The Third ◽  
Slow Roll ◽  
Klein Gordon ◽  
Early Universe Cosmology ◽  
Klein Gordon Equation

We study [Formula: see text] gravity models in the language of scalar–tensor (ST) theories. The correspondence between [Formula: see text] gravity and ST theories is revisited since [Formula: see text] gravity is a subclass of Brans–Dicke models, with a vanishing coupling constant ([Formula: see text]). In this treatment, four [Formula: see text] toy models are used to analyze the early-universe cosmology, when the scalar field [Formula: see text] dominates over standard matter. We have obtained solutions to the Klein–Gordon equation for those models. It is found that for the first model [Formula: see text], as time increases the scalar field decreases and decays asymptotically. For the second model [Formula: see text], it was found that the function [Formula: see text] crosses the [Formula: see text]-axis at different values for different values of [Formula: see text]. For the third model [Formula: see text], when the value of [Formula: see text] is small, the potential [Formula: see text] behaves like the standard inflationary potential. For the fourth model [Formula: see text], we show that there is a transition between [Formula: see text]. The behavior of the potentials with [Formula: see text] is totally different from those with [Formula: see text]. The slow-roll approximation is applied to each of the four [Formula: see text] models and we obtain the respective expressions for the spectral index [Formula: see text] and the tensor-to-scalar ratio [Formula: see text].

Inflationary constraints in teleparallel gravity theory

2020 ◽  
pp. 2150027
Author(s):  
Shambel Sahlu ◽  
Joseph Ntahompagaze ◽  
Amare Abebe ◽  
David F. Mota
Keyword(s):  
Observational Data ◽  
Spectral Index ◽  
Power Law ◽  
Teleparallel Gravity ◽  
Gravity Models ◽  
Index Formula ◽  
Scalar Tensor Theory ◽  
Tensor Theory ◽  
Slow Roll ◽  
Inflationary Parameters

In this work, the cosmological inflationary parameters in the correspondence of teleparallel gravity for the scalar–tensor theory are investigated. After the review of [Formula: see text] and [Formula: see text] gravity cosmology, we use the slow-roll approximations to study the behavior of the inflationary parameters namely the spectral index [Formula: see text] and tensor-to-scalar ratio [Formula: see text], and a comparison with observational data for different paradigmatic [Formula: see text] gravity models such as exponential, Linder and power-law models is considered. We also consider the boundary term [Formula: see text] associated with these three models. The obtained behavior of the parameters under consideration shows that it is possible to constrain [Formula: see text] and [Formula: see text] models based on observational data.

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