# isotropy

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• Nick:I like the isotropy of these...
• Jesse:Can you use a different word than 'isotropy'?

Note that, in the expansion of the Universe, what is expanding really is space-time. It is not that galaxies are running away from one another through a static space-time. At first approximation, galaxies are fixed in space and moving with it. Galaxies in reality do move through space-time, as we will see later, but this motion is small compared to the Hubble expansion and is sourced by small inhomogeneities. As the Hubble expansion is a stretching of space-time, there is no contradiction to find that at high redshift things seems to move at speeds comparable to the speed of light: no information is really moving through space-time at that speed (or faster). If we consider the expansion of the Universe and the homogeneity and isotropy properties, then it is useful to define a scale factor to describe the expansion. The distance r between any two points as a function of time t can be factorized as r(t) = r(t0)a(t), where a denotes the scale factor and r(t0) is the comoving coordinate. It is easy to see that the Hubble parameter is given by _a=a, where the dot denotes the time derivative. Also, it is easy to see that a = 1=(1 + z). It is easy to conclude that, if the Universe is expanding and its content is matter (dark or not) – and possibly curvature – gravity should slow down the expansion over time. Not only that, but by measuring the deceleration, one should be able to “weigh” the Universe! So it was a big surprise when, in 1998,
two teams [3,4] analysing their data came to the conclusion that the expansion was actually accelerating. Their measurements relied on surveying a particular type of exploding star and measuring their redshifts.
These exploding stars are “standard candles”, i.e. they all have the same intrinsic luminosity.1 The redshifts give the recession velocity, and the observed brightness of the standard candle (the intrinsic luminosity of which is known, and the same for all standard candles) gives an estimate of the distance. Thus, one can map the recession velocity as a function of distance, and trace the expansion history of the Universe. The principal investigators of the two teams received the Nobel Prize in Physics in 2011. The discovery of the accelerated expansion has changed the course of cosmology, with most major observational efforts today being devoted to understanding the acceleration.

[ Authors ]
Emanuela Dimastrogiovanni, Matteo Fasiello, Marc Kamionkowski
[ Abstract ]
Attention has focussed recently on models of inflation that involve a second or more fields with a mass near the inflationary Hubble parameter $H$, as may occur in supersymmetric theories if the supersymmetry-breaking scale is not far from $H$. Quasi-single-field (QSF) inflation is a relatively simple family of phenomenological models that serve as a proxy for theories with additional fields with masses $m\sim H$. Here we consider the tensor-scalar-scalar (tss) three-point function that arises in QSF inflation. Since QSF involves fields in addition to the inflaton, the consistency conditions between correlations that arise in single-clock inflation are not necessarily satisfied. As a result, the tensor-scalar-scalar correlation may be larger than in single-field inflation. This tss correlation gives rise to local departures from statistical isotropy, or in other words, a nontrivial four-point function. The presence of the tensor mode may moreover be inferred geometrically from the shape dependence of the four-point function. We estimate the size of a galaxy survey required to detect this tss correlation in QSF inflation as a function of $H$. Our study of primordial correlators which include gravitons in seeking imprints of additional fields with masses $m\sim H$ during inflation can be seen as complementary to the recent “cosmological collider physics” proposal.

Your Balancing Act for a Wholesome Life

We probe the possible anisotropy in the accelerated expanding Universe by using the JLA compilation of type-Ia supernovae. We constrain the amplitude and direction of anisotropy in the anisotropic cosmological models. For the dipole-modulated $\Lambda$CDM model, the anisotropic amplitude has an upper bound $D<1.04\times10^{-3}$ at the $68\%$ confidence level. Similar results are found in the dipole-modulated $w$CDM and CPL models. Our studies show that there are no significant evidence for the anisotropic expansion of the Universe. Thus the Universe is still well compatible with the isotropy.