Scalar Spectral Index Research Articles

Inflationary cosmology in [formula omitted] modified gravity

In this paper, we investigate the cosmological inflation scenario in the context of f(R,T) theory of gravity, where f is a generic function of the curvature scalar R and the trace T of the energy momentum tensor. Assuming that the slow roll inflation conditions hold true in f(R,T) gravity, we obtain from the Hubble slow roll parameters, the various inflation-related observables such as the tensor-to-scalar ratio r, the scalar spectral index ns, the running αs of the spectral index and the tensor spectral nT for two specific f(R,T) models. To see the viability of these models, a numerical analysis of such parameters has been done. The results show that by using the various values of free parameters it is possible to obtain a viable compatibility with the observational data.

A refined Einstein–Gauss–Bonnet inflationary theoretical framework

We provide a refined and much more simplified Einstein–Gauss–Bonnet inflationary theoretical framework, which is compatible with the GW170817 observational constraints on the gravitational wave speed. As in previous works, the constraint that the gravitational wave speed is in natural units, results to a constraint differential equation that relates the coupling function of the scalar field to the Gauss–Bonnet invariant ξ(ϕ) and the scalar potential V(ϕ). Adopting the slow-roll conditions for the scalar field and the Hubble rate, and in contrast to previous works, by further assuming that , which is motivated by slow-roll arguments, we succeed in providing much more simpler expressions for the slow-roll indices and for the tensor and scalar spectral indices and for the tensor-to-scalar ratio. We exemplify our refined theoretical framework by using an illustrative example with a simple power-law scalar coupling function ξ(ϕ) ∼ ϕ ν and as we demonstrate the resulting inflationary phenomenology is compatible with the latest Planck data. Moreover, this particular model produces a blue-tilted tensor spectral index, so we discuss in brief the perspective of describing the NANOGrav result with this model as is indicated in the recent literature.

Adiabatic duality: Duality of cosmological models with varying slow-roll parameter and sound speed

There have been thousands of cosmological models for our early universe proposed in the literature, and many of them claimed to be able to give rise to scale-invariant power spectrum as was favored by the observational data. It is thus interesting to think about whether there are some relations among them, e.g., the duality relation. In this paper, we investigate duality relations between cosmological models in framework of general relativity (GR) , not only with varying slow-roll parameter $\epsilon$, but also with sound speed $c_s$, which can then be understood as "adiabatic duality". Several duality relationships are formulated analytically and verified numerically. We show that models with varying $\epsilon$ and constant $c_s$ can be dual in scalar spectral index, but not tensor one. On the other hand, allowing both $\epsilon$ and $c_s$ to vary can make models dual in both scalar and tensor spectral indices.

Implication of the Hubble tension for the primordial Universe in light of recent cosmological data

In prerecombination resolutions of the Hubble tension, such as early dark energy, new physics before recombination shifts the values of relevant cosmological parameters so that the models can fit with cosmic microwave background and baryon acoustic oscillations observations as well as $\Lambda$CDM does. In this paper, we clarify how the parameter shifts are related with $\delta H_0$, particularly we find the shift of primordial scalar spectral index scales as ${\delta n_s}\simeq 0.4{\delta H_0\over H_0}$ by performing the Monte Carlo Markov chain analysis with the Planck2018+BAO+Pantheon+R19+Keck Array/BICEP dataset. A novel point of our result is that if the current $H_0$ measured locally is correct, complete resolution of the Hubble tension seems to be pointing to a scale invariant Harrison-Zeldovich spectrum, i.e. $n_s= 1$ for $H_0\sim 73$km/s/Mpc.

Inflation with R (αβ) terms in the Palatini formulation

We study inflation with the most general non-degenerate gravitational action that depends on the symmetric part of the Ricci tensor coupled to a scalar field in the Palatini formulation of gravity. We use field redefinitions to shift the effect of the Ricci terms from gravity to the scalar field, and apply the result to slow-roll inflation.As examples, we consider actions quadratic and cubic in the Ricci tensor. In the quadratic case the results are similar to the case R + α R 2 that has been studied earlier: the tensor-to-scalar ratio r can be suppressed by an arbitrary amount, while the scalar spectrum is unaffected. In the cubic case, r can be suppressed by at most a factor of 2/9, and the change in the scalar spectral index n s can be large.

On the α-attractor T-models

We carry out a fully analytical study of the phenomenology of α-attractor T-models defined by the potential V = V0tanhp(λϕ/M_pl). We obtain expressions for the number of e-folds during inflation Nke in terms of the scalar spectral index ns and independently in terms of the tensor-to-scalar ratio r. From these expressions we obtain exact solutions for both ns and r in terms of Nke along with their expansions for large Nke, in full agreement with known expressions. Eliminating the parameter λ from the model in terms of ns and r we can obtain exact solutions for r in terms of ns and Nke which allows us to reproduce, in particular, numerical solutions presented by the Planck Collaboration for the monomial potentials. We explicitly show how these solutions are contained in the solutions for the α-attractors and are also the end points of these. Finally, by also eliminating the global scale V0 in terms of the observables ns and r we show how in the appropriate limit the α-attractor potential exactly reduces to the monomials potential. We also briefly show that for α-attractor E-models, which generalize the Starobinsky potential in the Einstein frame, a similar transition occurs.

Viable intermediate inflation in the mimetic DBI model

We study the intermediate inflation in the mimetic Dirac–Born–Infeld model. By considering the scale factor as a=a_{0}exp (bt^{beta }), we show that in some ranges of the intermediate parameters b and beta , the model is free of the ghost and gradient instabilities. We study the scalar spectral index, tensor spectral index, and the tensor-to-scalar ratio in this model and compare the results with Planck2018 TT, TE, EE + lowE + lensing + BAO + BK14 data at 68% and 95% CL. In this regard, we find some constraints on the intermediate parameters that lead to the observationally viable values of the perturbation parameters. We also seek the non-Gaussian features of the primordial perturbations in the equilateral configuration. By performing the numerical analysis on the nonlinearity parameter in this configuration, we show that the amplitude of the non-Gaussianity in the intermediate mimetic DBI model is predicted to be in the range -16.7<f^{equil}<-12.5. We show that, with 0<ble 10 and 0.345<beta <0.387, we have an instabilities-free intermediate mimetic DBI model that gives the observationally viable perturbation and non-Gaussianity parameters.

Extracting cosmological parameters from N-body simulations using machine learning techniques

We make use of snapshots taken from the Quijote suite of simulations, consisting of 2000 simulations where five cosmological parameters have been varied (Ωm, Ωb, h, n s and σ8) in order to investigate the possibility of determining them using machine learning techniques. In particular, we show that convolutional neural networks can be employed to accurately extract Ω m and σ 8 from the N-body simulations, and that these parameters can also be found from the non-linear matter power spectrum obtained from the same suite of simulations using both random forest regressors and deep neural networks. We show that the power spectrum provides competitive results in terms of accuracy compared to using the simulations and that we can also estimate the scalar spectral index n s from the power spectrum, at a lower precision.

Attractor and slow roll parameterized inflation in extended teleparallel gravity

The study of inflation through different prospects is being done for specific model of scalar f(T) gravity in two phases such as attractor (ns(N)−1∝N−1) and slow roll parameterizations. In the presence of these ingredients, we evaluate all inflationary parameters such as scalar spectral index, tensor to scalar ratio r and running of scalar spectral index and local non Gaussianity parameter. We also develop the inflationary planes ns−N, r−N, dnsdlnκ−N, dnsdlnκ−ns and fNL−ns. These planes show the viability of our outcomes with Planck data 2018.

Preheating and reheating constraints in supersymmetric braneworld inflation

We study the evolution of the Universe at early stages, we discuss also preheating in the framework of hybrid braneworld inflation by setting conditions on the coupling constants $\lambda $ and $g$\ for effective production of $\chi$-particles. Considering the phase between the time observable CMB scales crossed the horizon and the present time, we write reheating and preheating parameters $N_{re}$, $T_{re}$ and $N_{pre}$ in terms of the scalar spectral index $n_{s}$, and prove that, unlike the reheating case, the preheating duration does not depend on the values of the equation of state $\omega ^{\ast }$. We apply the slow-roll approximation in the high energy limit to constrain the parameters of D-term hybrid potential. We show also that some inflationary parameters, in particular, the spectral index $n_{s}$ demand that the potential parameter $\alpha$ is bounded as $\alpha \geq 1$ to be consistent with $Planck$'s data, while the ratio $r$ is in agreement with observation for $ \alpha \leq 1 $ considering high inflationary e-folds. We also propose an investigation of the brane tension effect on the reheating temperature. Comparing our results to recent CMB measurements, we study preheating and reheating parameters $N_{re}$, $T_{re}$ and $N_{pre}$ in the Hybrid D-term inflation model in the range $0.8\leq \alpha\leq 1.1$\, and conclude that $T_{re}$ and $N_{re}$ require $\alpha \leq 1$, while for $N_{pre}$ the condition $\alpha \leq 0.9$ must be satisfied, to be compatible with $Planck$'s results.

Reconstructing inflation in scalar-torsion f(T,phi ) gravity

It is investigated the reconstruction during the slow-roll inflation in the most general class of scalar-torsion theories whose Lagrangian density is an arbitrary function f(T,phi ) of the torsion scalar T of teleparallel gravity and the inflaton phi . For the class of theories with Lagrangian density f(T,phi )=-M_{pl}^{2} T/2 - G(T) F(phi ) - V(phi ), with G(T)sim T^{s+1} and the power s as constant, we consider a reconstruction scheme for determining both the non-minimal coupling function F(phi ) and the scalar potential V(phi ) through the parametrization (or attractor) of the scalar spectral index n_{s}(N) and the tensor-to-scalar ratio r(N) as functions of the number of e-folds N. As specific examples, we analyze the attractors n_{s}-1 propto 1/N and rpropto 1/N, as well as the case rpropto 1/N (N+gamma ) with gamma a dimensionless constant. In this sense and depending on the attractors considered, we obtain different expressions for the function F(phi ) and the potential V(phi ), as also the constraints on the parameters present in our model and its reconstruction.

Inflation with non-canonical scalar fields revisited

We revisit inflation with non-canonical scalar fields by applying deformed-steepness exponential potentials. We show that the resulting scenario can lead to inflationary observables, and in particular to scalar spectral index and tensor-to-scalar ratio, in remarkable agreement with observations. Additionally, a significant advantage of the scenario is that the required parameter values, such as the non-canonicality exponent and scale, as well as the potential exponent and scale, do not need to acquire unnatural values and hence can accept a theoretical justification. Hence, we obtain a significant improvement with respect to alternative schemes, and we present distinct correlations between the model parameters that better fit the data, which can be tested in future probes. This combination of observational efficiency and theoretical justification makes the scenario at hand a good candidate for the description of inflation.

Holographic inflation in f(T) and DGP braneworld

In this paper, we investigate the holographic inflation in the framework of two gravitational theories like [Formula: see text] gravity, where [Formula: see text] corresponds to the torsion scalar and DGP braneworld model which is based on the idea that our four-dimensional FRW universe located on five-dimensional manifold. The modified infrared cutoff is used to explore all the inflationary parameters as slow-roll parameters [Formula: see text], number of [Formula: see text]-folds [Formula: see text], scalar spectral index [Formula: see text], tensor-to-scalar ratio [Formula: see text] and running of the scalar spectral index [Formula: see text]. Also, we investigate the behavior of inflationary parameters [Formula: see text] and [Formula: see text] through graphical presentation. The behavior of these parameters shows the consistency with Planck data [Formula: see text].

Construction of inflationary scenarios with the Gauss\u2013Bonnet term and nonminimal coupling

Inflationary models with a scalar field nonminimally coupled both with the Ricci scalar and with the Gauss–Bonnet term are studied. We propose the way of generalization of inflationary scenarios with the Gauss–Bonnet term and a scalar field minimally coupled with the Ricci scalar to the corresponding scenarios with a scalar field nonminimally coupled with the Ricci scalar. Using the effective potential, we construct a set of models with the same values of the scalar spectral index n_s and the amplitude of the scalar perturbations A_s and different values of the tensor-to-scalar ratio r.

Double peaks of gravitational wave spectrum induced from inflection point inflation

We investigate the possibility of inducing the gravitational waves (GWs) with double peak energy spectrum from primordial scalar perturbations in inflationary models with three inflection points. Here the inflection points can be generated from a polynomial potential or generated from a Higgs-like phi ^4 potential with the running of quartic coupling. In such models, the inflection point at large scales predicts the scalar spectral index and tensor-to-scalar ratio to be consistent with current CMB constraints, and the other two inflection points generate two large peaks in the scalar power spectrum at small scales, which can induce GWs with a double peak energy spectrum. We find that for some choices of the parameters the double peak spectrum can be detected by future GW detectors, and one of the peaks around fsimeq 10^{-9}{-}10^{-8} Hz can also explain the recent NANOGrav signal. Moreover, the peaks of the power spectrum allow for the generation of primordial black holes, which accounts for a significant fraction of dark matter.

Curing inflationary degeneracies using reheating predictions and relic gravitational waves

It is well known that the inflationary scenario often displays different sets ofdegeneracies in its predictions for CMB observables. These degeneracies usually arise either because multiple inflationary modelspredict similar values for the scalar spectral index n S and the tensor-to-scalarratio r, or because within the same model, the values of {n S , r}are insensitive to some of the model parameters, making it difficult for CMB observations alone to constitute a unique probe of inflationary cosmology. We demonstrate that by taking into account constraints on the post-inflationary reheating parameters such as the duration of reheating N re, its temperature T re and especially its equationof state (EOS), w re, it is possible to break this degeneracy in certain classes of inflationary models where identical values of {n S , r} can correspond to different reheating w re. In particular, we show how reheating constraints can break inflationary degeneracies in the T-model and the E-model α-attractors. Non-canonical inflation is also studied. The relic gravitational wave (GW) spectrum provides us with another tool to break inflationary degeneracies.This is because the GW spectrumis sensitiveto the post-inflationary EOS of the universe. Indeed a stiff EOS during reheating (w re > 1/3) gives rise to a small scale blue tilt in the spectral indexn GW = d log ΩGW/d log k > 0, while a soft EOS (w re < 1/3) results in a red tilt.Relic GWs therefore provide us with valuable information about the post-inflationary epoch, and their spectrumcan be used to cure inflationary degeneracies in {n S , r}.

Tsallis holographic dark energy for inflation

The application of holographic principle in very early time is studied. The consideration of the principle in the late-time evolution will be a good motivation to study its role at the time of inflation. Since the length scale is expected to be small during inflation, the resulted energy density form the holographic principle is expected to be large enough to drive inflation. The entropy of the system is the main part of the holographic principle, in which modifying entropy will leads to a modified energy density. Here, instead of the original entropy, we are going to apply a modified entropy, known as Tsallis entropy which includes quantum corrections. The length scale is assumed to be GO length scale. Finding an analytical solution for the model, the slow-roll parameters, scalar spectral index, and tensor-to-scalar ratio are calculated. Comparing the result, with Planck $r-n_s$ diagram, we could find a parametric space for the constants of the model. Then, a correspondence between the holographic dark energy and the scalar field is constructed, and the outcome potentials are investigated.

Cosmological inflation driven by a scalar torsion function

A viable model for inflation driven by a torsion function in a Friedmann background is presented. The scalar spectral index in the interval 0.92lesssim n_{s}lesssim 0.97 is obtained in order to satisfy the initial conditions for inflation. The post inflationary phase is also studied, and the analytical solutions obtained for scale factor and energy density generalizes that ones for a matter dominated universe, indicating just a small deviation from the standard model evolution. The same kind of torsion function used also describes satisfactorily the recent acceleration of the universe, which could indicate a possible unification of different phases, apart form specific constants

Inflationary cosmology- A new approach using Non-linear electrodynamics

We explore a new kind of NLED field as a source of gravity, which can accelerate the Universe during the inflationary era. We propose a new type of NLED lagrangian which is characterised by two parameters: α (dimensionless parameter) and β (dimensionful parameter). We investigate the classical stability and the causality aspects of this model of inflationary expansion by demanding that the speed of the sound wave and . Corresponding to , we find for α = 0.1(1.0). The equation of state parameter ω = −1/3 requires corresponding to . We find that the Universe is accelerating i.e. (which results in the deceleration parameter q < 0 (i.e. ω > −1/3)), provided . During inflation, the energy density is found to be maximum and is given by . The magnetic field necessary to trigger the inflation is found to be , where is the energy density of the Universe during the inflationary expansion. Our model also predicts the e-fold number that the magnetic field at the end of inflation is about B = 10−10 (10−4) Gauss corresponding to z = 0(1000) and this agrees quite well with the experimental prediction of the e-fold number. With α = 0.3(1.0) and , we find the scalar spectral index n s = 0.9649, consistent with the PLANCK 2018 CMB data. Further, with , we predicts the tensor-to-scalar ratio r = 0.1417(0.1449) and the tensorial spectral index .

A note on supergravity inflation in braneworld

We discuss supergravity inflation in braneworld cosmology for the class of potentials [Formula: see text] with [Formula: see text]. These minimal SUGRA models evade the [Formula: see text] problem due to a broken shift symmetry and can easily accommodate the observational constraints. In the high energy regime [Formula: see text], the numerical predictions and approximate analytic formulas are given for the scalar spectral index [Formula: see text] and tensor-to-scalar ratio [Formula: see text]. The models with smaller [Formula: see text] are preferred while the models with larger [Formula: see text] are out of the [Formula: see text] region. Remarkably, the [Formula: see text] correction to the energy density in Friedmann equation results in sub-Planckian inflaton excursions [Formula: see text].