Auditory Sleep Stimulation or Sham in People With Parkinson Disease Mild Cognitive Impairment During Cognitive Training

Inclusion Criteria: * clinical diagnosis of PD along the MDS criteria (Postuma et al., 2015) * MCI according to the MDS criteria, level I (Litvan et al., 2012): * \- cognitive decline: Gradual decline, in the context of established PD, in cognitive ability reported by either the patient or informant, or observed by the clinician, AND * \- MoCA ≤ 26 and ≥ 18 (Hoops et al., 2009) * stable home situation (e.g. long-term place to live) that allows for reliable application of intervention for the duration of the study * ability to apply the sleep intervention for the duration of study, either alone or with assistance of a co-habitant if needed * ability to apply the CogT intervention for the duration of study * sufficient German language comprehension to follow the study procedures and answer all questions related to the study outcomes * dosing of dopaminergic and other PD treatment must have been stable for at least 14 days prior to the intervention period and will be expected to remain stable until the end of the study. Exclusion Criteria: Diagnosis/Comorbidities: * clinical diagnosis of dementia (cognitive impairment sufficient to interfere with independence in everyday activities, i.e. "major neurocognitive disorder", DSM-5) * known presence of neurologic (other than PD) or psychiatric disorder * Parkinsonism without response to levodopa; atypical Parkinsonian syndromes as assessed from medical history and clinical examination * severe medical conditions (for example, renal insufficiency, liver failure, or congestive heart failure) as assessed in the semi-structured screening interview * regular use of benzodiazepines and other central nervous system (CNS)-depressant substances as assessed in the semi-structured screening interview * known or suspected drug- or medication abuse as assessed in the semi-structured screening interview * substance or alcohol abuse (i.e. \> 0.5 l wine or 1 l beer per day) as assessed in the semi-structured screening interview Sleep disorders that could interfere with the sleep intervention: * obstructive sleep apnea with apnea-hypopnea index (AHI)\>15, apnea-related NREM sleep fragmentation, and indication for treatment (in turn, primarily REM-related sleep apnea, not requiring specific treatment may be considered eligible); or use of continuous positive airway pressure (CPAP) * Restless Legs Syndrome * frequent (i.e. weekly) Non-REM sleep parasomnia (Sleep disorders typically associated with PD will not lead to exclusion, i.e. REM sleep behavior disorder, insomnia, nocturnal PD symptoms.) PTAS: * inability to hear the tones produced by the sleep headband (TOSOO Axora device) * non-responder to PTAS during screening (PTAS does not evoke a discernable auditory evoked potential AEP) * skin disorders/problems/allergies in face/ear area that could worsen with electrode application * known or suspected non-compliance Cognition \& informed consent: * inability to follow the procedures of the study, e.g. due to language problems, cognitive deficits * failure to give informed consent Other studies: * participation in another study with investigational interventions within 30 days (PTAS) or 1 year (CogT) preceding and during the present study * previous enrolment in the current study * enrolment of the investigator, his/her family members, employees and other dependent persons Special events / behavior with impact on circadian rhythm, sleep, or cognition: * shift work (work during the night) * travelling more than 2 time zones in the last month before intervention starts or during intervention (start of intervention will be adapted to fit with this criteria) * planned medical intervention of substantial relevance, e.g. surgery, during intervention (routine assessments, e.g. check-ups will be allowed) Pregnancy: * women who are pregnant or breastfeeding, * intention to become pregnant during the course of the study, * lack of safe contraception, defined as: Female participants of childbearing potential, not using and not willing to continue using a medically reliable method of contraception for the entire study duration, such as oral, injectable, or implantable contraceptives, or intrauterine contraceptive devices, or who are not using any other method considered sufficiently reliable by the investigator in individual cases. Please note that female participants who are surgically sterilized/hysterectomized or post-menopausal for longer than 1 year are not considered as being of child bearing potential.