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We consider fluctuations in a perfect irrotational fluid coupled to gravity in an Einstein static universe background. We show that the homogeneous linear perturbations of the scalar and metric fluctuations in the Einstein static universe…
Based on the gauge invariant variables proposed in our previous paper [K. Nakamura, Prog. Theor. Phys. vol.110 (2003), 723.], some formulae of the perturbative curvatures of each order are derived. We follow the general framework of the…
Classical determinations of galaxy distances and galaxy recessional velocities have been generated from luminosity and emission spectrometric data. The analyses of these galactic spectrometric electromagnetic frequency shifts have resulted…
In this paper we prove a global existence theorem, in the direction of cosmological expansion, for sufficiently small perturbations of a family of $n+1$-dimensional, $n \geq 3$, spatially compact spacetimes which generalizes the $k=-1$…
We consider different deductions of the mysterious Weinberg formula and show that this leads us back to the model of fluctuational cosmology which correctly predicted in advance, dark energy driven, accelerating universe with a small…
We derive the power spectrum of primordial quantum fluctuations in an inflationary universe for curvature parameter ${\mathcal K}=1$. This is achieved through a Born--Oppenheimer type of approximation scheme from the Wheeler--DeWitt…
Quantum gravitational effects in loop quantum cosmology lead to a resolution of the initial singularity and have the potential to solve the horizon problem and generate a quasi scale-invariant spectrum of density fluctuations. We consider…
We consider the non-commutative inflation model of [3] in which it is the unconventional dispersion relation for regular radiation which drives the accelerated expansion of space. In this model, we study the evolution of linear cosmological…
We present the first steps needed for an analysis of the perturbations that occur in the cosmology associated with the conformal gravity theory. We discuss the implications of conformal invariance for perturbative coordinate gauge choices,…
The evolution equation of cosmic density perturbation of a spin dominated universe in Einstein-Cartan gravity is obtained.Examples of inflationary cosmologies with spin are also given where we compute the density perturbations in terms of…
We review how we can construct the gravity models which reproduces the arbitrary development of the universe. We consider the reconstruction in the Einstein gravity coupled with generalized perfect fluid, scalar-Einstein gravity,…
The Maxwell extension of the conformal algebra is presented. With the help of gauging the Maxwell-conformal group, a conformally invariant theory of gravity is constructed. In contrast to the conventional conformally invariant actions, our…
It is shown that a first-order relativistic perturbation theory for the open, flat or closed Friedmann-Lemaitre-Robertson-Walker universe admits one, and only one, gauge-invariant quantity which describes the perturbation to the energy…
We propose a way to construct manifestly gauge independent quantities out of the gauge dependent quantities occurring in the linearized Einstein equations. Thereupon, we show that these gauge-invariant combinations can be identified with…
We study the evolution of quantum fluctuations of a scalar field which is coupled to the geometry, in an exponentially expanding universe. We derive an expression for the spectrum of intrinsic perturbations, and it is shown that the…
All Lorentz invariant solutions of vacuum Einstein's equations are found. It is proved that these solutions describe space-times of constant curvature.
The genus of the iso-density contours is a robust measure of the topology of large scale structure, and it is relatively insensitive to nonlinear gravitational evolution, galaxy bias and redshift-space distortion. We show that the growth of…
We present the growing mode solutions of cosmological perturbations to the second order in the matter dominated era. We also present several gauge-invariant combinations of perturbation variables to the second order in most general fluid…
: From the epoch of recombination $(z\approx 10^3)$ till today, the typical density contrasts have grown by a factor of about $10^6$ in a Friedmann universe with $\Omega=1$. However, during the same epoch the typical gravitational potential…
We present the leading order non-linear density and velocity power spectra in the complete form; previous studies have omitted the vector- and tensor-type perturbations simultaneously excited by the scalar-type perturbation in nonlinear…