Shinji Tsujikawa

We discuss observational consequences of $f(R)$ dark energy scenarios that satisfy local gravity constraints (LGC) as well as conditions of the cosmological viability. The model we study is given by $m(r)=C(\ensuremath{-}r\ensuremath{-}1{)}^{p}$ ($C>0$, $p>1$) with $m=R{f}_{,RR}/{f}_{,R}$ and $r=\ensuremath{-}R{f}_{,R}/f$, which covers viable $f(R)$ models proposed so far in a high-curvature region designed to be compatible with LGC. The equation of state of dark energy exhibits a divergen

We derive the equation of matter density perturbations on subhorizon scales for a general Lagrangian density $f(R,\ensuremath{\phi},X)$ that is a function of a Ricci scalar $R$, a scalar field $\ensuremath{\phi}$, and a kinetic term $X=\ensuremath{-}(\ensuremath{\nabla}\ensuremath{\phi}{)}^{2}/2$. This is useful to constrain modified gravity dark energy models from observations of large-scale structure and weak lensing. We obtain the solutions for the matter perturbation ${\ensuremath{\delta}}_{

We study the evolution of (phantom) dark energy universe by taking into account the higher-order string corrections to Einstein–Hilbert action with fixed dilaton and modulus fields. While the presence of a cosmological constant gives stable de Sitter fixed points in the cases of heterotic and bosonic strings, no stable de Sitter solutions exist when a phantom fluid is present. We find that the universe can exhibit a Big Crunch singularity with a finite time for type II string, whereas it reaches

We consider the construction of nonsingular pre-big-bang and ekpyrotic type cosmological models realized by the addition to the action of specific higher-order terms stemming from quantum corrections. We study models involving general relativity coupled to a single scalar field with a potential motivated by the ekpyrotic scenario. We find that the inclusion of the string loop and quantum correction terms in the string frame makes it possible to obtain solutions of the variational equations which

We construct a family of viable scalar-tensor models of dark energy (DE) which possess a phase of late-time acceleration preceded by a standard matter era, while at the same time satisfying the local gravity constraints (LGC). The coupling $Q$ between the scalar field and the nonrelativistic matter in the Einstein frame is assumed to be constant in our scenario, which is a generalization of $f(R)$ gravity theories corresponding to the coupling $Q=\ensuremath{-}1/\sqrt{6}$. We find that these mod

We study the growth of matter density perturbations ${\ensuremath{\delta}}_{m}$ for a number of viable $f(R)$ gravity models that satisfy both cosmological and local gravity constraints, where the Lagrangian density $f$ is a function of the Ricci scalar $R$. If the parameter $m\ensuremath{\equiv}R{f}_{,RR}/{f}_{,R}$ today is larger than the order of ${10}^{\ensuremath{-}6}$, linear perturbations relevant to the matter power spectrum evolve with a growth rate $s\ensuremath{\equiv}d\mathrm{ln}{\e

In loop quantum cosmology, the universe avoids a big bang singularity and undergoes an early and short super-inflation phase. During super-inflation, non-perturbative quantum corrections to the dynamics drive an inflaton field up its potential hill, thus setting the initial conditions for standard inflation. We show that this effect can raise the inflaton high enough to achieve sufficient e-foldings in the standard inflation era. We analyse the cosmological perturbations generated when slow-roll

We make a detailed study of matter density perturbations in both metric and Palatini formalisms. Considering general theories whose Lagrangian density is a general function, $f(R)$, of the Ricci scalar $R$, we derive the equation of matter density perturbations in each case, in a number of gauges, including comoving, longitudinal and uniform density gauges. We show that for viable $f(R)$ models that satisfy cosmological and local gravity constraints (LGC), matter perturbation equations derived u

We study cosmological perturbations in generalized Einstein scenarios and show the equivalence of inflationary observables both in the Jordan frame and the Einstein frame. In particular the consistency relation relating the tensor-to-scalar ratio with the spectral index of tensor perturbations coincides with the one in Einstein gravity, which leads to the same likelihood results in terms of inflationary observables. We apply this formalism to nonminimally coupled chaotic inflationary scenarios w