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Extra resources for Introduction to the theory of the early unvierse: cosmological perturbations and inflationary theory
Sample text
Of course, these properties are well-known from electrodynamics, where the vectors e(+) and e(−) are circular polarization vectors of photon. Let us use the vectors e(1) and e(2) to construct two symmetric transverse traceless basis tensors 1 (+) (1) (1) (2) (2) eij = √ ei ej − ei ej 2 1 (×) (1) (2) (2) (1) eij = √ ei ej + ei ej . , they have helicities +2 and −2. , a mixture of helicities +2 and −2. 3. Prove the last statements above. 4. , that it transforms trivially under rotations around k-axis.
2 · 102 Mpc. 1. Repeat the above analysis of conformal times for dark energy equation of state pDE = wDE ρDE , where wDE is time-independent. 1. 73. , the present value of the Hubble parameter). Nevertheless, the conformal times of epochs in question are independent of the time we live, as should be the case. 13a) and change the integration variable to temperature T . 4). 25) This expression involves only quantities referring to the early Universe. It shows, in particular, that barring exotic relativistic component, the only relevant parameter is ΩM /Ωrad ≡ Teq /T0 .
A(T× ) q(T× ) T0 T× 11 In inflationary theory, even modes of the present wavelengths much exceeding H −1 were super0 horizon early at inflation. 5in Introduction to the Theory of the Early Universe: Cosmological Perturbations. . 3. Thus, perturbations of all interesting wavelengths were indeed subhorizon at the Hot Big Bang epoch. , somewhat larger than the size of the Solar system. There is a simple relation between the conformal momentum k of a wave and the conformal time η× at which this wave enters the horizon.