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 ( 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 ψ˙ = ∂R ∂C , π˙ = − ∂C − ∂R ∂C , N ∂π ∂R N ∂ψ ∂ψ ∂R into which I can substitute ∂C = 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 , ωR a˙ = −σβp¯√|β|, ψ = σβ π √|β|, π˙ ∂C = − , (5.61) ωψa3 = p¯˙ −1 ∂C 6a |β| a2 + a2 − 2ω √ ( σβp¯2 kωR R a6
Cosmology. 2.5.1 Studying AGN vs Starburst evolution along cosmic times
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 P ∫ √ M 2R where g = det(gµν).
(1.1) and using the Bianchi identity, the Einstein equations imply the continuity equation ∇µT = 0 . (1.3) Modern cosmology is based on the evidence that at large scale (larger than 300 million light years [11]) the universe is homogeneous and isotropic. Different ex- periments have corroborated these assumptions. One is the identically observed temperature of the CMB, another is the distribution of galaxies around us mea- sured by the 2dF Galaxy Redshift Survey [12] (see Fig. (1.1)).
Figure 1.1: Each dot is a galaxy with the Earth in the center of the map. It shows the spatial distribution of galaxies as a function of redshift from the 2dF Galaxy Redshift Survey [12]. On small scales the distribution is inhomogeneous but becomes more homogeneous on large scales. dθ
(1.4) Our universe is expanding with time, galaxies move away from each other as time passes. Then we can decompose space-time in slices of constant time that are ho- mogeneous and isotropic (foliation). The metric for such a universe is called the Xxxxxxxxx–Xxxxˆxxxx–Xxxxxxxxx–Xxxxxx (FRW) metric [13, 14] = −dt + a(t) 1 − Kr2 + r
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 d4x P ∫ √ M 2R where g = det(gµν).
(1.1) and using the Bianchi identity, the Einstein equations imply the continuity equation ∇µT = 0 . (1.3) Modern cosmology is based on the evidence that at large scale (larger than 300 million light years [11]) the universe is homogeneous and isotropic. Different ex- periments have corroborated these assumptions. One is the identically observed temperature of the CMB, another is the distribution of galaxies around us mea- sured by the 2dF Galaxy Redshift Survey [12] (see Fig. (1.1)).
Figure 1.1: Each dot is a galaxy with the Earth in the center of the map. It shows the spatial distribution of galaxies as a function of redshift from the 2dF Galaxy Redshift Survey [12]. On small scales the distribution is inhomogeneous but becomes more homogeneous on large scales. dθ
