Starobinsky Model Research Articles

Dark matter admixed strange quark stars in the Starobinsky model

The properties of dark matter admixed strange quark stars are investigated in the Starobinsky model of modified gravity. For quark matter we assume the MIT bag model, while self-interacting dark matter inside the star is modelled as a Bose-Einstein condensate with a polytropic equation of state. We numerically integrate the structure equations in the Einstein frame adopting the two-fluid formalism treating the curvature correction term non-perturbatively. Our findings show that strange quark stars (in agreement with current observational constraints) with the highest masses are equally affected by dark matter and modified gravity.

Dark stars in Starobinsky’s model

In the present work we study non-rotating dark stars in $f(R)$ modified theory of gravity. In particular, we have considered bosonic self-interacting dark matter modelled inside the star as a Bose-Einstein condensate, while as far as the modified theory of gravity is concerned we have assumed Starobinsky's model $R+aR^2$. We solve the generalized structure equations numerically, and we obtain the mass-to-ratio relation for several different values of the parameter $a$, and for two different dark matter equation-of-states. Our results show that the dark matter stars become more compact in the R-squared gravity compared to General Relativity, while at the same time the highest star mass is slightly increased in the modified gravitational theory. The numerical value of the highest star mass for each case has been reported.

Observational signatures of the parametric amplification of gravitational waves during reheating after inflation

We study the evolution of Gravitational Waves (GWs) during and after inflation as well as the resulting observational consequences in a Lorentz-violating massive gravity theory with one scalar (inflaton) and two tensor degrees of freedom. We consider two explicit examples of the tensor mass $m_g$ that depends either on the inflaton field $\phi$ or on its time derivative $\dot{\phi}$, both of which lead to parametric excitations of GWs during reheating after inflation. The first example is Starobinsky's $R^2$ inflation model with a $\phi$-dependent $m_g$ and the second is a low-energy-scale inflation model with a $\dot{\phi}$-dependent $m_g$. We compute the energy density spectrum $\Omega_{\rm GW}(k)$ today of the GW background. In the Starobinsky's model, we show that the GWs can be amplified up to the detectable ranges of both CMB and DECIGO, but the bound from the big bang nucleosynthesis is quite tight to limit the growth. In low-scale inflation with a fast transition to the reheating stage driven by the potential $V(\phi)=M^2 \phi^2/2$ around $\phi \approx M_{\rm pl}$ (where $M_{\rm pl}$ is the reduced Planck mass), we find that the peak position of $\Omega_{\rm GW}(k)$ induced by the parametric resonance can reach the sensitivity region of advanced LIGO for the Hubble parameter of order 1 GeV at the end of inflation. Thus, our massive gravity scenario offers exciting possibilities for probing the physics of primordial GWs at various different frequencies.

Restrictions on Extended Gravity at Galaxy Clusters Scales

Following [1] we discuss the predictions of Starobinsky model of f(R)-gravity with vanishing cosmological constant at galaxy and galaxy clusters scales. As a result we demonstrate that at the current observational accuracy level there is no significant difference in cut-off radius values for Starobinsky model and general relativity (GR) in the mass range from 109MS un till galaxy clusters ones (1018MS un) that shows the good applicability of GR at these ranges.

Non-Abelian cosmic string in the Starobinsky model of gravity

In this paper, we analyze numerically the behavior of the solutions corresponding to a non-Abelian cosmic string in the framework of the Starobinsky model, i.e. where [Formula: see text]. We perform the calculations for both an asymptotically flat and asymptotically (anti)-de Sitter spacetimes. We found that the angular deficit generated by the string decreases as the parameter [Formula: see text] increases, in the case of a null cosmological constant. For a positive cosmological constant, we found that the cosmic horizon is affected in a nontrivial way by the parameter [Formula: see text].

Equation-of-state of neutron stars with junction conditions in the Starobinsky model

We study the Starobinsky or [Formula: see text] model of [Formula: see text] for neutron stars with the structure equations represented by the coupled differential equations and the polytropic type of the matter equation-of-state (EoS). The junction conditions of [Formula: see text] gravity are used as the boundary conditions to match the Schwarzchild solution at the surface of the star. Based on these the conditions, we demonstrate that the coupled differential equations can be solved directly. In particular, from the dimensionless EoS [Formula: see text] with [Formula: see text] and [Formula: see text] and the constraint of [Formula: see text], we obtain the minimal mass of the NS to be around 1.44 [Formula: see text]. In addition, if [Formula: see text] is larger than 5.0, the mass and radius of the NS would be smaller.

Constraining f(R) gravity in solar system, cosmology and binary pulsar systems

The f(R) gravity can be cast into the form of a scalar–tensor theory, and scalar degree of freedom can be suppressed in high-density regions by the chameleon mechanism. In this article, for the general f(R) gravity, using a scalar–tensor representation with the chameleon mechanism, we calculate the parametrized post-Newtonian parameters γ and β, the effective gravitational constant Geff, and the effective cosmological constant Λeff. In addition, for the general f(R) gravity, we also calculate the rate of orbital period decay of the binary system due to gravitational radiation. Then we apply these results to specific f(R) models (Hu–Sawicki model, Tsujikawa model and Starobinsky model) and derive the constraints on the model parameters by combining the observations in solar system, cosmological scales and the binary systems.

No cosmic rays from curvature oscillations during structure formation in F(R) gravity

The Starobinsky model of modified gravity suggested to explain dark energy may be also considered in the astrophysical context. Recently it has been pointed out that in contracting regions curvature oscillations around the GR value may lead to the production of high energy particles which contribute to the cosmic ray flux. We revisit these calculations in the Einstein frame and show that the continuous approximation for the matter density used in the original calculations is not valid. We show that this problem is generic in $F(R)$-gravity models introduced to describe the dark energy. We go beyond the approximation and find the rate of particle production to be negligible.

Extranatural inflation redux

The success of a given inflationary model crucially depends upon two features: its predictions for observables such as those of the Cosmic Microwave background (CMB) and its insensitivity to the unknown ultraviolet (UV) physics such as quantum gravitational effects. Extranatural inflation is a well motivated scenario which is insensitive to UV physics by construction. In this five dimensional model, the fifth dimension is compactified on a circle and the zero mode of the fifth component of a bulk $U(1)$ gauge field acts as the inflaton. In this work, we study simple variations of the minimal extranatural inflation model in order to improve its CMB predictions while retaining its numerous merits. We find that it is possible to obtain CMB predictions identical to those of e.g. ${\cal R} + {\cal R}^2$ Starobinsky model of inflation and show that this can be done in the most minimal way by having two additional extra light fermionic species in the bulk, with the same $U(1)$ charges. We then find the constraints that CMB observations impose on the parameters of the model.

Anisotropic solutions in modified gravity

Anisotropic but homogeneous, shear-free cosmological models with imperfect matter sources in f(R) gravity are investigated. The relationship between the anisotropic stresses and the electric part of the Weyl tensor, as well as their evolutions in orthogonal f(R) models, is explored. The late-time behaviour of the de Sitter universe (as an example of a locally rotationally symmetric spacetimes in orthonormal frames) in f(R) gravity is examined. By taking initial conditions for the expansion, acceleration and jerk parameters from observational data, numerical integrations for the evolutionary behavior of the Universe in the Starobinsky model of f(R) have been carried out.

Reconstructing a f(R) theory from the α-Attractors

We show an analogy at high curvature between a f(R) = R + aRn − 1 + bR2 theory and the α-Attractors. We calculate the expressions of the parameters a, b and n as functions of α and the predictions of the model f(R) = R + aRn − 1 + bR2 on the scalar spectral index ns and the tensor-to-scalar ratio r. We find that the power law correction Rn − 1 allows for a production of gravitational waves enhanced with respect to the one in the Starobinsky model, while maintaining a viable prediction on ns. We numerically reconstruct the full α-Attractors class of models testing the goodness of our high-energy approximation f(R) = R + aRn − 1 + bR2. Moreover, we also investigate the case of a single power law f(R) = γ R2 − δ theory, with γ and δ free parameters. We calculate analytically the predictions of this model on the scalar spectral index ns and the tensor-to-scalar ratio r and the values of δ which are allowed from the current observational results. We find that −0.015 < δ < 0.016, confirming once again the excellent agreement between the Starobinsky model and observation.

Deforming the Starobinsky model in ghost-free higher derivative supergravities

We consider higher derivative supergravities that are dual to ghost-free $N=1$ supergravity theories in the Einstein frame. The duality is implemented by deforming the K\"ahler function, and/or the superpotential, to include nonlinear dependences on chiral fields that in other approaches play the role of the Lagrange multipliers employed to establish this duality. These models are of the no-scale type, and in the minimal case, require the presence of four chiral multiplets, with a K\"ahler potential having the structure of the $ SU(4,1)/SU(4) \times U(1) $ coset manifold. In the standard $N=1$ supergravity formulation, these models are described by a multifield scalar potential, featuring Starobinsky-like behavior in particular directions.

Abelian cosmic string in the extended Starobinsky model of gravity

We analyze numerically the behaviour of the solutions corresponding to an Abelian cosmic string taking into account an extension of the Starobinsky model, where the action of general relativity is replaced by $f(R) = R - 2\Lambda + \eta R^2 + \rho R^m$, with $m > 2$. As an interesting result, we find that the angular deficit which characterizes the cosmic string decreases as the parameters $\eta$ and $\rho$ increase. We also find that the cosmic horizon due to the presence of a cosmological constant is affected in such a way that it can grows or shrinks, depending on the vacuum expectation value of the scalar field and on the value of the cosmological constant

Analytic solution of the Starobinsky model for inflation

We prove that the field equations of the Starobinsky model for inflation in a Friedmann–Lemaître–Robertson–Walker metric constitute an integrable system. The analytical solution in terms of a Painlevé series for the Starobinsky model is presented for the case of zero and nonzero spatial curvature. In both cases the leading-order term describes the radiation era provided by the corresponding higher-order theory.

Starobinsky-like inflation, supercosmology and neutrino masses in no-scale flipped SU(5)

We embed a flipped SU(5) × U(1) GUT model in a no-scale supergravity framework, and discuss its predictions for cosmic microwave background observables, which are similar to those of the Starobinsky model of inflation. Measurements of the tilt in the spectrum of scalar perturbations in the cosmic microwave background, ns, constrain significantly the model parameters. We also discuss the model's predictions for neutrino masses, and pay particular attention to the behaviours of scalar fields during and after inflation, reheating and the GUT phase transition. We argue in favor of strong reheating in order to avoid excessive entropy production which could dilute the generated baryon asymmetry.

Starobinsky cosmological model in Palatini formalism

We classify singularities in FRW cosmologies, which dynamics can be reduced to the dynamical system of the Newtonian type. This classification is performed in terms of the geometry of a potential function if it has poles. At the sewn singularity, which is of a finite scale factor type, the singularity in the past meets the singularity in the future. We show that such singularities appear in the Starobinsky model in f({hat{R}})={hat{R}}+gamma {hat{R}}^2 in the Palatini formalism, when dynamics is determined by the corresponding piecewise-smooth dynamical system. As an effect we obtain a degenerate singularity. Analytical calculations are given for the cosmological model with matter and the cosmological constant. The dynamics of model is also studied using dynamical system methods. From the phase portraits we find generic evolutionary scenarios of the evolution of the universe. For this model, the best fit value of Omega _gamma =3gamma H_0^2 is equal 9.70times 10^{-11}. We consider a model in both Jordan and Einstein frames. We show that after transition to the Einstein frame we obtain both the form of the potential of the scalar field and the decaying Lambda term.

R + \u03b1Rn inflation in higher-dimensional space-times

We generalise Starobinsky’s model of inflation to space-times with D > 4 dimensions, where D − 4 dimensions are compactified on a suitable manifold. The D-dimensional action features Einstein-Hilbert gravity, a higher-order curvature term, a cosmological constant, and potential contributions from fluxes in the compact dimensions. The existence of a stable flat direction in the four-dimensional EFT implies that the power of space-time curvature, n, and the rank of the compact space fluxes, p, are constrained via n = p = D/2. Whenever these constraints are satisfied, a consistent single-field inflation model can be built into this setup, where the inflaton field is the same as in the four-dimensional Starobinsky model. The resulting predictions for the CMB observables are nearly indistinguishable from those of the latter.

Inverse symmetric inflationary attractors

We present a class of inflationary potentials which are invariant under a special symmetry, which depends on the parameters of the models. As we show, in certain limiting cases, the inverse symmetric potentials are qualitatively similar to the α-attractors models, since the resulting observational indices are identical. However, there are some quantitative differences which we discuss in some detail. As we show, some inverse symmetric models always yield results compatible with observations, but this strongly depends on the asymptotic form of the potential at large e-folding numbers. In fact when the limiting functional form is identical to the one corresponding to the α-attractors models, the compatibility with the observations is guaranteed. Also, we find the relation of the inverse symmetric models with the Starobinsky model and we highlight the differences. In addition, an alternative inverse symmetric model is studied and as we show, not all the inverse symmetric models are viable. Moreover, we study the corresponding F(R) gravity theory and we show that the Jordan frame theory belongs to the R2 attractor class of models. Finally, we discuss a non-minimally coupled theory and we show that the attractor behavior occurs in this case too.

Magnetogenesis during inflation and preheating in the Starobinsky model

By assuming the kinetic coupling $f^{2}(\phi)FF$ of the effective inflaton field $\phi$ with the electromagnetic field, we explore magnetogenesis during the inflation and preheating stages in the Starobinsky model. We consider the case of the exponential coupling function $f(\phi)=\exp(\alpha\phi/M_{p})$ and show that for $\alpha \sim 12-15$ it is possible to generate the large scale magnetic fields with strength $\gtrsim 10^{-15}$ Gauss at the present epoch. The spectrum of generated magnetic fields is blue with the spectral index $n=1+s$, $s>0$. We have found that for the relevant values of the coupling parameter, $\alpha=12-15$, model avoids the back-reaction problem for all relevant modes.

Inflation from the finite scale gauged Nambu–Jona-Lasinio model

The possibility to construct an inflationary universe scenario for the finite-scale gauged Nambu–Jona-Lasinio model is investigated. This model can be described by the Higgs–Yukawa type interaction model with the corresponding compositeness scale. Therefore, the one-loop Higgs–Yukawa effective potential is used with the compositeness condition for the study of inflationary dynamics. We evaluate the fluctuations in the cosmic microwave background for the model with a finite compositeness scale in the slow-roll approximation. We find the remarkable dependence on the gauge group and the number of fermion flavors. It is also proved that the model has similar behavior with the ϕ4n chaotic inflation and the Starobinsky model at the flat and steep limits, respectively. It is demonstrated that realistic inflation consistent with Planck data is possible for a range of theory parameters.