Editing Cosmic inflation (section)

===Fine-tuning problem===
One of the most severe challenges for inflation arises from the need for [[Fine-tuning (physics)|fine tuning]]. In new inflation, the ''slow-roll conditions'' must be satisfied for inflation to occur. The slow-roll conditions say that the inflaton [[scalar potential|potential]] must be flat (compared to the large vacuum energy) and that the inflaton particles must have a small mass.{{Clarify |reason=the inflaton particle has not been defined. From the note, it seems that the second condition should be that the inflaton potential should be large |date=June 2014}}{{efn|
Technically, these conditions are that the [[logarithmic derivative]] of the potential, <math>\ \epsilon = \tfrac{1}{2} \left(\tfrac{ V' }{ V }\right)^2\ </math> and second derivative <math>\ \eta = \tfrac{ V''}{ V }\ </math> are both small, where <math>\ V\ </math> is the potential, and the equations are written in [[reduced Planck units]].<ref>{{harvp|Liddle |Lyth|2000|pp=42–43}}</ref>
}}
New inflation requires the Universe to have a scalar field with an especially flat potential and special initial conditions. However, explanations for these fine-tunings have been proposed. For example, classically scale invariant field theories, where scale invariance is broken by quantum effects, provide an explanation of the flatness of inflationary potentials, as long as the theory can be studied through [[perturbation theory]].<ref>
{{cite journal
 |last1=Salvio  |first1=Alberto
 |last2=Strumia |first2=Alessandro |author-link2=Alessandro Strumia
 |date=17 March 2014
 |title=Agravity
 |journal=[[Journal of High Energy Physics]]
 |volume=2014 |issue=6 |page=80
 |arxiv=1403.4226 |bibcode=2014JHEP...06..080S
 |doi=10.1007/JHEP06(2014)080 |s2cid=256010671
}}
</ref>

Linde proposed a theory known as ''[[Chaotic inflation theory|chaotic inflation]]'' in which he suggested that the conditions for inflation were actually satisfied quite generically. Inflation will occur in virtually [[Multiverse|any universe]] that begins in a chaotic, high energy state that has a scalar field with unbounded potential energy.<ref name=chaotic>
{{cite journal
 |last=Linde |first=Andrei D.
 |date=1983
 |title=Chaotic inflation
 |journal=[[Physics Letters B]]
 |volume=129 |issue=3 |pages=171–81
 |bibcode=1983PhLB..129..177L
 |doi=10.1016/0370-2693(83)90837-7
}}
</ref>
However, in his model, the inflaton field necessarily takes values larger than one [[Planck unit]]: For this reason, these are often called ''large field'' models and the competing new inflation models are called ''small field'' models. In this situation, the predictions of [[effective field theory]] are thought to be invalid, as [[renormalization]] should cause large corrections that could prevent inflation.{{efn|
Technically, this is because the inflaton potential is expressed as a Taylor series in <math>\ \tfrac{ \mathrm{\phi} }{ m_\mathsf{Plk} }\ ,</math> where <math>\ \mathrm{\phi}\ </math> is the inflaton and <math>\ m_\mathsf{Plk}\ </math> is the [[Planck mass]]. While for a single term, such as the mass term <math>\ m^4_\mathrm{\phi} \left( \tfrac{ \mathrm{\phi} }{ m_\mathsf{Plk} }\right)^2\ ,</math> the slow roll conditions can be satisfied for <math>\ \mathrm \phi\ </math> much greater than <math>\ m_\mathsf{Plk}\ ,</math> this is precisely the situation in effective field theory in which higher order terms would be expected to contribute and destroy the conditions for inflation. The absence of these higher order corrections can be seen as another sort of fine tuning.<ref>
{{cite journal
 |last1=Alabidi |first1=Laila
 |last2=Lyth    |first2=David H.
 |year=2006
 |title=Inflation models and observation
 |journal=[[Journal of Cosmology and Astroparticle Physics]]
 |volume=2006  |issue=5  |page=016
 |arxiv=astro-ph/0510441  |bibcode=2006JCAP...05..016A
 |doi=10.1088/1475-7516/2006/05/016  |s2cid=119373837
}}
</ref>
}}
This problem has not yet been resolved and some cosmologists argue that the small field models, in which inflation can occur at a much lower energy scale, are better models.<ref>
{{cite journal
 |last=Lyth |first=David H.
 |year=1997
 |title=What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy?
 |journal=[[Physical Review Letters]]
 |volume=78 |issue=10 |pages=1861–1863
 |arxiv=hep-ph/9606387 |bibcode=1997PhRvL..78.1861L
 |s2cid=119470003 |doi=10.1103/PhysRevLett.78.1861
 |url=http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+EPRINT+HEP-PH/9606387
 |archive-url=https://archive.today/20120629010941/http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+EPRINT+HEP-PH/9606387
 |archive-date=2012-06-29
}}
</ref>
While inflation depends on quantum field theory (and the [[semiclassical gravity|semiclassical approximation]] to [[quantum gravity]]) in an important way, it has not been completely reconciled with these theories.

[[Robert Brandenberger|Brandenberger]] commented on fine-tuning in another situation.<ref>
{{cite conference
 |first=Robert H. |last=Brandenberger  |author-link=Robert Brandenberger
 |date=November 2004
 |title=Challenges for inflationary cosmology
 |conference=10th International Symposium on Particles, Strings, and Cosmology
 |arxiv=astro-ph/0411671
}}
</ref>
The amplitude of the primordial inhomogeneities produced in inflation is directly tied to the energy scale of inflation. This scale is suggested to be around {{10^|16}} [[GeV]] or {{10^|−3}} times the [[Planck energy]]. The natural scale is naïvely the Planck scale so this small value could be seen as another form of fine-tuning (called a [[hierarchy problem]]): The energy density given by the scalar potential is down by {{10^|−12}} compared to the [[Planck density]]. This is not usually considered to be a critical problem, however, because the scale of inflation corresponds naturally to the scale of gauge unification.