Exploring the parameter space of modified supergravity for double inflation and primordial black hole formation

We study the parameter space of the effective (with two scalars) models of cosmological inflation and primordial black hole (PBH) formation in the modified $(R+R^2)$ supergravity. Our models describe double inflation, whose first stage is driven by Starobinskys scalaron coming from the $R^2$ gravity, and whose second stage is driven by another scalar belonging to the supergravity multiplet. The ultra-slow-roll regime between the two stages leads a large peak (enhancement) in the power spectrum of scalar perturbations, which results in efficient PBH formation. Both inflation and PBH formation are generic in our models, while those PBH can account for a significant part or the whole of dark matter. Some of the earlier proposed models in the same class are in tension (over $3sigma$) with the observed value of the scalar tilt $n_s$, so that we study more general models with more parameters, and investigate the dependence of the cosmological tilts $(n_s,r)$ and the scalar power spectrum enhancement upon the parameters. The PBH masses and their density fraction (as part of dark matter) are also calculated. A good agreement (between $2sigma$ and $3sigma$) with the observed value of $n_s$ requires fine tuning of the parameters, and it is only realized in the so-called $delta$-models. Our models offer the (super)gravitational origin of inflation, PBH and dark matter together, and may be confirmed or falsified by future precision measurements of the cosmic microwave background radiation and PBH-induced gravitational waves.

Study on charged strange stars in $fleft(R,mathcal{T}right)$ gravity

We investigate effects of the modified $f(R, mathcal{T})$ gravity on the charged strange quark stars with the standard choice of $f(R, mathcal{T})=R+2chi mathcal{T}$. Those types of stars are supposed to be made of strange quark matter (SQM) whose distribution is governed by the phenomenological MIT bag EOS as $p=frac{1}{3}(rho-4B)$, where $B$ is the bag constant, while the form of charge distribution is chosen to be $qleft(rright)=Qleft(r/Rright)^3=alpha r^3$ with $alpha$ as a constant. We derive the values of the unknown parameters by matching the interior spacetime to the exterior Reissner-Nordstr{o}m metric followed by the appropriate choice of the values of the parameters $chi$ and $alpha$. Our study reveals that besides SQM, a new kind of matter distribution originates due to the interaction between the matter and the extra geometric term, while the modification of the Tolman-Oppenheimer-Volkoff (TOV) equation invokes the presence of a new force $F_c$. The accumulation of the electric charge distribution reaches its maximum at the surface, and the predicted values of the corresponding electric charge and electric field are of the order of $10^{19-20}$ C and $10^{21-22}$ V/cm, respectively. To examine the physical validity of our solutions, we perform several tests and find that the proposed $f(R, mathcal{T})$ model survives all these critical tests. Therefore, our model can describe the non-singular charged strange stars and justify the supermassive compact stellar objects having their masses beyond the maximum mass limit for the compact stars in the standard scenario. Our model also supports the existence of several exotic astrophysical objects like super-Chandrasekhar white dwarfs, massive pulsars, and even magnetars, which remain unexplained in the framework of General Relativity (GR).

Exploring physical features of anisotropic strange stars beyond standard maximum mass limit in $fleft(R,mathcal{T}right)$ gravity

We study a specific model of anisotropic strange stars in the modified $fleft(R,mathcal{T}right)$-type gravity by deriving solutions to the modified Einstein field equations representing a spherically symmetric anisotropic stellar object. We take a standard assumption that $f(R,mathcal{T})=R+2chimathcal{T}$, where $R$ is Ricci scalar, $mathcal{T}$ is the trace of the energy-momentum tensor of matter, and $chi$ is a coupling constant. To obtain our solution to the modified Einstein equations, we successfully apply the `embedding class 1 techniques. We also consider the case when the strange quark matter (SQM) distribution is governed by the simplified MIT bag model equation of state given by $p_r=frac{1}{3}left(rho-4Bright)$, where $B$ is bag constant. We calculate the radius of the strange star candidates by directly solving the modified TOV equation with the observed values of the mass and some parametric values of $B$ and $chi$. The physical acceptability of our solutions is verified by performing several physical tests. Interestingly, besides the SQM, another type of matter distribution originates due to the effect of coupling between the matter and curvature terms in the $fleft(R,mathcal{T}right)$ gravity theory. Our study shows that with decreasing the value of $chi$, the stellar systems under investigations become gradually massive and larger in size, turning them into less dense compact objects. It also reveals that for $chi<0$ the $fleft(R,mathcal{T}right)$ gravity emerges as a suitable theory for explaining the observed massive stellar objects like massive pulsars, super-Chandrasekhar stars and magnetars, etc., which remain obscure in the standard framework of General Relativity (GR).

Quantizing with a higher time derivative

We review the classical and quantum theory of the Pais-Uhlenbeck oscillator as the toy-model for quantizing f(R) gravity theories.