research10.1016/j.physletb.2014.06.017

Axion dark matter with high-scale inflation

Abstract

We show that supersymmetric axion models breaking the PQ symmetry by the interplay of non-renormalizable supersymmetric terms and soft supersymmetry breaking terms provide a natural framework not only for generating the axion scale from soft supersymmetry breaking scale <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>m</mi></mrow><mrow><mn>3</mn><mo stretchy="false">/</mo><mn>2</mn></mrow></msub></math> but also for enhancing it during inflation by factor of order <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><msub><mrow><mi>H</mi></mrow><mrow><mi>I</mi></mrow></msub><mo stretchy="false">/</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>3</mn><mo stretchy="false">/</mo><mn>2</mn></mrow></msub></mrow></msqrt></math> where <math altimg="si3.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>H</mi></mrow><mrow><mi>I</mi></mrow></msub><mo>≃</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>14</mn></mrow></msup><mtext> </mtext><mtext>GeV</mtext></math> according to the recent BICEP2 result. In this scheme, the PQ symmetry can stay broken throughout the whole history of the Universe if the reheat temperature is below <math altimg="si4.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mn>10</mn></mrow><mrow><mn>10</mn></mrow></msup><mtext> </mtext><mtext>GeV</mtext></math> , or <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>m</mi></mrow><mrow><mn>3</mn><mo stretchy="false">/</mo><mn>2</mn></mrow></msub></math> when the PQ fields couple strongly to thermal (Standard Model) particles. It is also shown that parametric resonance during preheating is not effective enough to induce non-thermal PQ symmetry restoration. As a consequence, axion models with the QCD anomaly <math altimg="si5.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>N</mi></mrow><mrow><mi>D</mi><mi>W</mi></mrow></msub><mo>&gt;</mo><mn>1</mn></math> can be made free from the domain wall problem while the axion isocurvature perturbation is suppressed sufficiently for the axion scale during inflation larger than about <math altimg="si6.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>M</mi></mrow><mrow><mi>P</mi></mrow></msub><msup><mrow><mo stretchy="false">(</mo><msub><mrow><mi>Ω</mi></mrow><mrow><mi>a</mi></mrow></msub><msup><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy="false">/</mo><mn>0.12</mn><mo stretchy="false">)</mo></mrow><mrow><mn>1</mn><mo stretchy="false">/</mo><mn>2</mn></mrow></msup><msup><mrow><mo stretchy="false">(</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>a</mi></mrow></msub><mo stretchy="false">/</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>12</mn></mrow></msup><mtext> </mtext><mtext>GeV</mtext><mo stretchy="false">)</mo></mrow><mrow><mn>0.6</mn></mrow></msup><mtext> </mtext><mtext>GeV</mtext></math>

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