Cosmology. To find the cosmological dynamics, I restrict to a flat, homogeneous, and isotropic metric in proper time (N = 1). I also assume that β does not depend on the minimally coupled scalar field φ for the sake of simplicity. From (3.37), I find the Xxxxxxxxx equation, which can be written in two equivalent forms, R R 2 β 2 R ψ2 + H (ω H + ω′ ψ˙) = 1 ( ωψ ψ˙2 + ωφ φ˙2 + σ √|β| U ) , (3.38a) ( 1 ′ ˙)2 1 [ 1 ( ω ωRH + ωRψ = ωRωψ + |β| U 3 ′ ) ˙ ωRωφ √ ] R φ˙2 + σβωR
Cosmology. In this section I find the cosmological implications of the nearest order corrections coming from the deformation to general covariance. Since it is a perturbative expansion, the results when the corrections become large should be taken to be indicative rather than predictive. I restrict to a flat FLRW metric as in section 2.8, L = −a U (a) − N 2√|β | H
Cosmology. I restrict to an isotropic and homogeneous space to find the background cosmological dynamics, following the definitions in section 2.8. Writing the constraint as C = C(a, ψ, R) where R = R(a, ψ, p¯, π), the equations of motion are given by, a˙ = 1 ∂R ∂C , p¯˙ = −1 ( ∂C + ∂R ∂C ) , N 6a ∂p¯ ∂R N 6a ∂a ∂a ∂R (5.60) ψ˙ = ∂R ∂C , π˙ = − ∂C − ∂R ∂C , N ∂π ∂R N ∂ψ ∂ψ ∂R into which I can substitute ∂C ∂R = a3√|β|. When I assume minimal coupling (ωR′ = 0, ωψ′ = 0) and time-symmetry (ξ = 0), the equations of motion become, −3σβp¯2 3 kωR σβπ2 ψ ˙ R → ωRa2 − a2 + 2ω a6 , N ωR a˙ = −σβp¯√|β|, ψ = σβ π √|β|, π˙ ∂C N ∂ψ = − , (5.61) N ωψa3 = N ∂a − a p¯˙ −1 ∂C 6a |β| a2 + a2 − 2ω √ ( σβp¯2 kωR ω R a6 .
Cosmology. In 1915, Xxxxxxxx published his equations of motion of gravity [10] Rµν − 2 gµνR = 8πGTµν , (1.1) where G is the gravitational constant (G = 6.67 × 10−11m3kg−1s−2), Rµν the Ricci tensor, R the Ricci scalar and Tµν the stress energy tensor. The left hand side of the equation is related to the metric and determines the space-time curvature of the universe, whereas the right hand side is given by the matter content of the universe. Einstein equations of motion in vacuum can be derived from the Xxxxxxxx-Xxxxxxx action by varying the action with respect to the metric gµν Sg = d4x −g P , (1.2) ∫ √ M 2R where g = det(gµν).
Cosmology. 2.5.1 Studying AGN vs Starburst evolution along cosmic times Our perspective of galaxy evolution has greatly changed in recent years thanks to two main findings: the first is the the so-called Magorrian relation (see Section 2.4). The second is the evidence that most, if not all, galaxies during their evolution pass through a dust-obscured bright FIR/submillimetre phase. The first finding strongly suggests that in order to understand galaxy evolution in galaxies one has to study the evolution of the non-thermal nuclear activity (AGN) - on one side - and of star formation (SF) - on the other side. The second finding shows that the far-IR spectral domain is the most adequate to study galaxy evolution at the maximum of its activity - both AGN and SF - by overcoming dust obscuration and observing the peak continuum emission. The starburst emission regions in galaxies has a linear size of 1-2 kpc and can be resolved at any redshift using FIR interferometry reaching an angular resolution of 0.1 arcsec. In fact, as shown in Fig.9, beyond the redshift z=2, due to the standard cosmology, the apparent size of astrophysical objects starts to increase as a function of redshift.We will therefore be able with FIRI to study both photometrically and specroscopically how the starburst components evolve in cosmic times. Whilst the AGN Narrow line Regions will not be resolved beyond z=0.1, spectroscopy will still allow to disentangle starburst and AGN components through bright fine structure lines. FIGURE 9: ANGULAR SIZES OF THE RELEVANT FIR EMITTING COMPONENTS OF GALAXIES AS A FUNCTION OF REDSHIFT, FOLLOWING THE STANDARD COSMOLOGICAL MODEL (SPERGEL ET AL. 2007).
