What is the evidence for Inflation of the early universe? The theory of Inflation explains the apparent consistency of the universe by proposing that  the early universe grew exponentially for a 1E-36 seconds. Isn't a simpler explanation that the universe is just older and so the homogeneousness comes from a slower more steady growth? Is there any evidence that rules out a slow growing universe and supports Inflation theory?
 A: As pointed out by Weinberg in his book Cosmology (note, this is NOT Gravitation and Cosmology. He also has a book of that name), inflation was proposed to explain 3 problems:
1)Horizon problem
2)Flatness problem
3)Monopole problem
1)Horizon problem: The evolution of the scale factor before and after decoupling is $\sqrt{t}$ and $t^{\frac{2}{3}}$. We compute the linear dimension of the forward and backward lightcones at the time of decoupling in the hot big bang model. The radius of this light cone is the physical size of the region on the last scattering surface from which we receive the CMB. The backward lightcone is $l_{B} \approx 3(t_{dec}^{2}t_{0})^{1/3}$ ($t_{0}$ is present time.). The forward lightcone radius is $l_{F} = 2t_{dec}$. The ratio $R \equiv \frac{l_{B}}{l_{F}} \approx 70$. The physical wavelength associated with cosmological perturbations grows faster than the Hubble radius as we go back in time. If, a causal mechanism is responsible for the inhomogenities, then these scales should be inside Hubble scale in very early universe. This is possible if, the perturbation associated wavelength decreases faster than Hubble radius as we go back in time. So, $-\frac{d}{dt}\left( \frac{\lambda}{d_{H}}\right) <0 $ ($d_{H}$ is the Hubble radius). This leads to $\ddot{a} >0$. In most cases, we model it as a single scalar field which causes this inflation in a de Sitter background ($\Lambda$ dominated universe)
2)Flatness problem: A less convincing argument of inflation. Experimentally, we observe a vanishing spatial curvature parameter $\Omega_{K} = -\frac{K}{a^2 H^2} = -\frac{K}{a^2}$. In solving this problem, we assume that nothing much happens to the cosmic scale factor and expansion rate from the end of inflation to the beginning of the radiation dominated era i.e $a_{Inflation}H_{Inflation} \approx a_{rad. domination}H_{rad. domination}$. The small value of $|K|/\dot{a}^2$ could be explained by taking $K=0$ i.e a spatially flat universe. However, inflation opens up the possibility that the universe is not at all homogenous and isotropic and that its apparent flatness of the cosmic metric is just the result of inflation.
3)Monopole problem: Standard Model predicts that in a hot early universe, a large number of monopoles must be produced by symmetry breaking from some single gauge theory since it is at an energy scale of about $M = 10^{16}$ GeV. Those monopoles should have persisted even to the present days. However, that is not the case. 
Amongst all the above problems, the horizon problem is the most serious one. Since, the other two can be explained by other mechanisms. Also, any number of $e$-foldings not only solves the horizon problem but also the flatness problem and the monopole problem.
A: I can not go into much detail here but let me say that exponential growth brings many things that we see around us right now: absence of magnetic monopoles, a homogeneous universe in which no section is a "preferred" section i.e. has more matter density, and many more observable quantities.
Actually after a brief search I found a wiki article stating most of the things i said above and much, much more: http://en.wikipedia.org/wiki/Cosmic_inflation#Observational_status
A: Personally I think the standard arguments are not yet conclusive. The horizon problem, or the homogeneity problem, can be explained by assuming that the initial condition is homogeneous, without assuming that causal contact in the early universe has smoothed out inhomogeneities. You may object that a homogeneous initial condition is "unnatural", but since we know so little about the big bang singularity, there's nothing conclusive that can be said. The monopole problem is only a problem if you think monopoles exist, which has no empirical evidence so far. The curvature problem, again, is a "naturalness" problem, but we lack a precise definition of naturalness given our inability to understand the big bang singularity.
A: The main (and original) reason for the proposal of inflationary theory was the horizon problem. That is, the fact the the universe is so incredibly homogeneous and isotropic despite the fact that some parts of the universe are apparently too far away to have exchanged energy. Inflation in the early universe is a powerful explanation for this intriguing observation. Also of note is the flatness problem, which inflation also helps address.
There are of course various other theories to explaining this problems, not in any way related to inflation, such as the varying speed of light (VSL) theory. These are however under active research and still not widely accepted.
A: The evidence is against:
CMB WMAP maps are inconsistent with the standard cosmological model, from here:    
Large-angle anomalies in the CMB (open access) and in arXiv - April 2010 (my bold)    

Abstract
  ...We discuss these findings in relation to expectation
  from standard inflationary cosmology ...
  Summary
  The study of alignments in the low ℓ CMB has found a
  number of peculiarities. We have shown that the alignment of the
  quadrupole and octopole planes is inconsistent with Gaussian,
  statistically isotropic skies at least at the 99% confidence
  level. Further a, number of (possibly related) alignments occur at
  95% confidence levels or greater. Putting together these provides
  a strong indication that the full-sky CMB WMAP maps are inconsistent
  with the standard cosmological model at the large-angles. Even
  more peculiar is the alignment of the quadrupole and octopole with
  solar system features (the ecliptic plane and the dipole).
Introduction
  In this regard, it is worth noting that our record at
  predicting the gross properties of the universe on large scales from
  first principles has been rather poor. According to the standard
  concordance model of cosmology, over 95% of the energy content of the
  universe is extraordinary—dark matter or dark energy whose existence
  has been inferred from the failure of the Standard Model of particle
  physics plus General Relativity to describe the behavior of
  astrophysical systems larger than a stellar cluster—while the very
  homogeneity and isotropy (and inhomogeneity) of the universe owe to
  the influence of an inflaton field whose particle-physics-identity is
  completely mysterious even after three decades of theorizing.
Conclusions   ... The CMB is widely regarded as offering strong
  substantiating evidence for the concordance model of cosmology. Indeed
  the agreement between theory and data is remarkable—the patterns in
  the two-point correlation functions (TT, TE, and EE) of Doppler peaks
  and troughs are reproduced in detail by fitting with only six (or so)
  cosmological parameters. This agreement should not be taken lightly;
  it shows our precise understanding of the causal physics on the last
  scattering surface. Even so, the cosmological model we arrive at is
  baroque, requiring the introduction at different scales and epochs of
  three sources of energy density that are only detected
  gravitationally—dark matter, dark energy and the inflaton. This
  alone should encourage us to continuously challenge the model and
  probe the observations particularly on scales larger than the horizon
  at the time of last scattering.
At the very least, probes of the large-angle (low-ℓ) properties of the
  CMB reveal that we do not live in a typical realization of the
  concordance model of inflationary ΛCDM.


On the theoretical side: from Michael S. Turner (1997)
Ten Things Everyone Should Know About Inflation

Cold dark matter, which is an important means of testing inﬂation, is
  a ten-parameter theory, $h,\Omega_Bh^2,S,n,dn/d \ln{k}, T/S, nT,
> \Omega_\nu,g_*, \Omega_\Lambda$ . While this is a daunting number of
  parameters, especially for a cosmological theory, there is good
  reason to believe that within ten years the data will
  overdetermine these parameters. Crucial to achieving this goal are the
  high-precision, high-resolution measurements of CBR anisotropy that
  will be made over the next decade by...
  ...ΛCDM is consistent with all the observations discussed here as well as others;...
  ...
Inﬂation Makes Three Robust Predictions
  1 Flat universe
  2 Nearly scale-invariant spectrum of gaussian density perturbations
  3 Nearly scale-invariant spectrum of gravitational waves  


The future: (obviously it is my own perspective)
In this novel cosmological model A self-similar model of the Universe unveils the nature of dark energy the Inflation is not needed.
I had a part in the paper, not as an author, and I appreciate any criticism  

